It is barely light when I open my eyes, a pale greyness around the edges of the curtains suggesting it is about an hour before dawn. The bedside clock says 5:24. It is my room, but it is different – things are in different positions on the walls, the atmosphere is unusual. I can't pin down why, exactly, but although I know I'm not where I should be, it still feels like home. The covers feel different as well, more constricted, as I turn to look at the clock. Not my clock, I realise.

My breath catches in my throat as I lie back and become more aware, still for a moment – I am not alone in the bed.

I don't panic. Which is curious, because I think I should panic. After all, there shouldn't be anyone in my bed with me, and it is my bed. It is where my bed should be: in the middle, halfway between window on the left and door on the right, head to the internal wall. Wardrobe to the left at the bottom; chest-of-drawers to the right near the door. My bed in my bedroom, although not my bed covers and not my hangings on the walls and that strange feeling of not myself being in the right place.

And someone else in bed with me.

She is remarkably beautiful. She is lying mostly on her front, her face turned towards me and half-hidden under a disarrayed mess of dark, curly hair; her full lips are slightly apart and the light breath of her sleep disturbs strands of the hair. Her cheeks are well-defined but not sharp, and she has a gentle nose and chin. Her bare arm is in the middle of the bed, atop the covers, and it was this, I realise, which had constricted them as I'd moved to look at the clock. She looks familiar, like a face half-remembered from a decade ago; somehow I know she is called Katie, that she is Katie – but I know I have never seen her before.

At least, the "I" who knows this is someone else's room imposed on my own, who recognises where she is but doesn't know why that place is not where it should be, who would never wake up with another woman...this "I" knows she has never seen Katie before. The other "I", who does know this room and doesn't feel out of place in it...she obviously does know who Katie is. Although I am not sure who that other girl is, this other I.

Yet I still don't feel alarmed, let alone panicked. In fact, I feel comfortable. But still different. Like I am not in my own life, but it is all right. As if I can live with it, until I can explain it.

Very gently, so as not to wake Katie, I lift the covers and slide out of the bed. I notice I am naked, with detached surprise because I never sleep naked, although it doesn't actually feel very surprising here. To make certain, I lift the covers again and satisfy my curiosity for something I already know: Katie is also naked. For a moment, I consider that this Katie is beautiful in many ways.

I look around for my nightgown, and of course fail to see anything like it, so take an oversize t-shirt from the pile of clothes spilling from the chair near the door and cover myself. The t-shirt smells of Katie. I make my way confidently along the landing and downstairs to the kitchen – and notice that this unfamiliar new reality is certainly my house, because I can not only find my way in the pre-dawn gloom without thinking, but even instinctively avoid the creaky floorboard on the landing and the creaky step near the bottom of the stairs. The kitchen is of course not mine, although the fittings are all where they normally are.

I pour a glass of water and drink it slowly, wandering around the kitchen and living room. My guitar is on the sofa, a pad of manuscript paper under the neck – I pick the pad up, dislodging a pencil, and hum through the melody, which is transcribed in my hand: it is new but familiar, and the words underlying it are a love song, also in my handwriting. It's a nice tune, and its familiarity is mysterious – like everything in this house which is mine but not mine. I put the pad and pencil back, and assume I wrote the song, although I have no idea when or why.

On the mantelpiece are a couple of years' worth of pictures of me and Katie in situations and clothes I feel are very unlikely – especially for me. Katie looks beautiful in each one. There are accumulated souvenirs of a shared life amongst them, and others on the bookcases. Many of the books are familiar, I know they are mine, but others are presumably Katie's: books on art and art history and technique, amongst other things. (Presumably Katie's? Of course they are.) On the walls are paintings and sketches in decent but cheap frames, which I somehow know are by Katie, or chosen by her.

The sofa and chairs are not mine, but are in the right place. The small portable organ I inherited from my great-aunt is in its normal corner: I have it and use it because there is no room for a piano, but it also has sentimental value. Seeing it in its familiar place in this unfamiliar environment makes me smile and want to cry at the same time. I haven't cried for years, and I'm not known for laughing a lot either, but somehow that seems unlike me now.

Upstairs, I find the spare room is an artist's workshop. Amongst a stash of drawings in a portfolio case are some incomplete sketches of various things, but mainly portraits of a young woman with long fair hair – some from the back, some from the front or side; some clothed, or semi-clothed; many naked. I look more carefully at a head-and-shoulders study in semi-profile, and recognise myself. I have the same scar on my chin from when I fell into a fence as a child. The affection with which the drawing has been executed makes me want to smile and cry again.

Replacing the drawings carefully, I cross to the bathroom and check in the mirror: I am certainly still me. In fact, almost the only definite constant in this whole strange early morning is my appearance, down to and including the scar.

I refill my glass in the kitchen, and pour a second, and return to the bedroom. Putting the second glass on Katie's side of the bed, I put my glass on my side and strip off the t-shirt. (When did I ever think about having a side of the bed? Or casually undressing with someone?) Katie mumbles something as I lift the cover and slide myself back into the bed gently, and I tell her to go back to sleep.

"I'm awake now, Ursula," she says, opening one eye carefully. Somehow I know I've always loved her eyes, even though I do not know who she is. "What time is it?"

The clock says 5:41, I tell her.

She sighs and snakes her arm round my waist. We kiss, and suddenly she is much more awake. Even as I pull her close to me I tell her that I need to get up soon, get ready for work. She glances at the clock as she moves further on top of me, her knee pushing my thighs apart, her body moving against mine. "Not yet, you don't."

*****

A bright dawn is showing around the curtains. Ursula starts awake at 7:02, and stares at her familiar clock on her familiar bedside cabinet in her familiar bedroom. She knows she is alone in the bed, and stretches out on her back to consider that for a minute. She decides she must have had a dream – a particularly vivid dream – and feels bereft for a moment at the lingering memory of the companionship it had shown her.

Her eyes flick to the crucifix on the wall by the door, and she flushes with the usual feelings of shame and guilt. She gets up and – taking the rosary she keeps looped around it – kneels below it to go through the familiar prayers, hoping particularly for forgiveness for the pleasure the dream had given her. She knows the girls at school, and some of her fellow teachers, call her "Sister Ursula" behind her back in a mocking reference to her piety – but they are unaware how hard and how often she has to atone for her shameful desires, or how long she has been denying them.

Some spiritual equilibrium temporarily restored, she gets herself ready and takes herself off to the Catholic boarding school on the outskirts of town, at which she is the music mistress. On the bus journey there, she fingers the small silver crucifix around her neck each time her mind slips back to the dream. She notes that the dream is, unusually, losing none of its vivid sharpness, as if it were truly like slipping into another life.

After supper that evening, she practises the organ and tries to write a new hymn for the school choir. Whenever she tries to turn the tune to the chosen text, however, it turns itself back to the melody in the dream. Giving up – giving in to the force of it – she finds her guitar and sits on the sofa to sing it through to herself, eyes closed, somehow remembering the words perfectly and almost feeling as if she were back in that other room, on that other sofa.

*****

As the last chord dies, a soft voice says, "Lovely, Ursula."

I open my eyes slowly, and see Katie smiling from the opposite end of the sofa. Her bare feet are tucked underneath her. She's in the denim shorts and t-shirt she often wears for working in – the same t-shirt I had borrowed that morning. Her thick hair is out of the way in a careless bun, a pencil stuck through it. I look down and find that my normal demure skirt and blouse have become the short, summery dress from one of the mantlepiece photos. Katie leans over and kisses me, then gets up and fetches us both a glass of wine. She shows me the drawings she's made for one of her latest commissions. I like the comfort of our home life, the safety of her love which I can be confident of coming home to each day. Unlike the austere, judgemental "love" I know in my real existence (the only love I know there), Katie allows me to feel safe and secure, and fulfilled and whole. I feel blessed to know her.

I tell her so.

"And me you," she says, kissing me again and resting a hand affectionately on my thigh. "I'm so glad I got to you before you took the job in that dreary old school. You'd be miserable in that life. And we wouldn't have this." Her hand moves between my thighs and she kisses me differently. "Now, do you think it's time for an early night?"

I say yes.

*****

The following morning, Ursula kneels below her crucifix and cries in anguish for deliverance.

From the bus on the way home that afternoon, she sees a young woman with dark hair wearing Katie's t-shirt, carrying an artist's portfolio case. Ursula stumbles from her seat to stop the bus, and runs after her. "Katie!"

The stranger turns, surprised, and stares at Ursula for a moment, head on one side. "I've literally just moved here," she says carefully. "How do you know my name?" She frowns and reaches up to trace Ursula's scar gently with her thumb, then smiles. She begins humming Ursula's tune, and Ursula hums the end of the phrase. "Mysterious. You're called Ursula, aren't you?"