What's in the water in Yorkshire? That place has produced the likes of Michael Palin and Alan Bennett, both still boyish in their old age, still with full heads of hair, sharp wit and a glint in the eye. There must be something brilliant in the water.

But in Remember Me (BBC1) the water in Yorkshire has turned sinister. Old Tom is haunted by something which makes its presence felt via dripping taps, leaking window frames and visions of drowning.

This is a new three-part drama for Sunday nights, but forget the froth and fluff we're usually given on these slow evenings. This is something entirely different: a classic ghost story, brilliantly acted, which is also odd, dreamlike and sometimes shocking.

The story opens with Tom (Michael Palin), an old man living alone in a dingy Yorkshire backstreet. He carefully lies down at the foot of his stairs, allowing his neighbour to find him and think he's had a fall. Social Services arrive and suggest taking him to a nursing home. 'Are you going to make your mind up or what?' he snaps at the social worker in his haste to be gone from the house. He is desperate to leave and takes nothing with him but an empty suitcase.

Woven between these opening scenes was a glimpse of something horrific on a beach. We see a cold and windy shore. A silent black figure is lying on the sand. It begins to move and slowly gets to its feet.

The story then switches back to Tom. He has been cheerfully settled into the nursing home. When the alarm goes off in his room, the social worker rushes upstairs to help. The residents below hear awful crashes from his room and the electricity flickers. Seconds later, the social worker is discovered outside, having fallen to her death from Tom's window. 'I should have stopped her,' says Tom. Stopped whom? We don't know.

Old Tom is moved into hospital. His care worker, Hannah, thinks she's being helpful by collecting some clothes from his house but he is horrified. He refuses to touch anything from the house. His fear worsens when he learns Hannah explored the house and played 'Scarborough Fair' on his old piano. She protests that she didn't touch any of the old sheet music, but he says 'you brought it away in your heart! Now you can never take it back.'

He considers the contents of the house as tainted or cursed in some way. That's why he was desperate to leave and why he took nothing with him. Now the curse has infected Hannah and she starts to be plagued by nightmares of a figure on the beach and terrible visions of drowning. Meanwhile, Tom has fled the hospital and can't be traced.

Remember Me sometimes verged on the histrionic, but this was always tempered by flashes of realism. For every creaking floorboard we had a scene with Hannah's alcoholic mother. For every flickering candle we had the tough cop Skyping his daughter in Australia. For all the bleak Yorkshire scenery of abandoned mills, black trees and rushing water we had portakabins, motorways and bus stops. This pinned the story to the ground and stopped it flying off into ghostly melodrama.

Although an intriguing story in its own right, and a welcome change from the usual Sunday night costume dramas, Remember Me borrowed too much from classic MR James ghost stories. It was laden with cobwebs, creaking floorboards, flickering candles and sudden draughts to set the curtains moving and the creepy rocking chair going.

You could also feel the heavy influence of The Shining (Hannah riffling through the stacks of identical sheet music, the shell thrown silently to Tom, the water cascading down the stairs), The Woman In Black (the ghostly figure advancing on Hannah's bed), Under The Skin (visions of Hannah silently kicking and flailing under water) and, of course, lots of nods to the Japanese version of The Ring. There were perhaps too many influences elbowing their way in, and they threatened to swamp the story.

Nonetheless, Remember Me was very entertaining and atmospheric - so much so that it simply didn't need to exploit all those creaky floorboards and flickering candles. There was a risk of over-egging the pudding with too much eerie Victoriana. The story and the fine acting would have been sturdy enough without it. However, there were enough shocks and surprises and subplots to keep me intrigued and keen to see the next two episodes.