Fancy a date with an artist? Always longed for a work which was unique to you? A new BBC series brings artists to clients, famous and ordinary. It is a match, Lindsay Calder discovers, which could be heaven or hell.

Remember when you used to come home from school and proudly present your mother with the latest creation from your art lesson, and how she would feign delight and stick it to the kitchen wall before saying "It's lovely darling... what is it?"

This is Rebecca's reaction when Cornelia reveals the pieces of art she has made specially for Rebecca. Except Rebecca is not Mummy, she is Rebecca Stephens, the first British woman to climb Everest, and Cornelia is not a satchel-toting school kid, she is Cornelia Parker, short-listed for tomorrow's Turner Prize.

How did these two come together you might ask? Well, BBC2 have fixed them up on Date with an Artist. This is the first in a series of six programmes, where the BBC and the Arts Council, acting as a sort of creative dating agency, pair up 12 contemporary artists with 12 new patrons. The deal is that the two spend time together, get to know each other, then the artist goes off to produce a work of art for their new BBC buddy. The end result is the surprise element.

When I first heard about the idea for this programme I imagined a sort of home decoration swap where an unknown artist would turn up at a suburban villa and do a quick, made-to-measure, colour co-ordinated painting for the lounge-diner. Along the lines of: "Well, the carpet's blue, and the curtains are yellow, I love a bit of sunflower spread, and Brian lost his ear in an accident, so I wondered if you could do us some Van Gogh- style sunflowers to fit in the up-lit alcove?"

But no, it's all a bit more Sensational than that. Among the hot dates in the artist/patron line-up over the next few weeks is Chris Ofili (elephant dung "Sensation" boy) paired with a prisoner from Wormwood Scrubs; and Jake and Dinos Chapman (X-rated "Sensation" duo of children-with-penises- for-noses fame) paired with Justine Frishmann, lead singer with Elastica. These are not the sort of people who have lounge-diners.

Rebecca Stephens does have a lounge. In fact she has rather a nice flat. She is not some fleece-wearing, weather-beaten old hard nut whose hallway is blocked with crampons, tents and great big boots. She is Nanette Newman- ish with shoulder-length hair, flowery feminine clothes and sofas with cushions on. (The Everest gear is neatly concealed in her under-bed storage boxes.) Cornelia and Rebecca seem to hit it off, and giggle their way through most of the programme like two slightly tipsy flatmates. After they have rifled through Rebecca's boxes they head for the giddy heights of St Paul's Cathedral - certainly giddy for Cornelia who has a fear of heights but feels the climbing up high thing is essential for her commission. Just watch Cornelia as jolly Rebecca leans over the railing at the top in her halter-neck top and her summer skirt. Small beer compared to Everest, but a bit of a mammoth cocktail for Cornelia who seems to be much happier rooting about on the floor collecting fluff.

In fact Cornelia is rather like a 10-year-old schoolboy - at the stage of collecting beastly things and keeping them in jars and matchboxes. Like many of her contemporaries she is preoccupied with death, waste and ultimately relics. She has in her collection naval fluff, a poet's gold crown and a feather from Freud's famous couch. For Cornelia, detritus and remains are infused with a great significance. The fluff from the Whispering Gallery is "acoustic build up" of "ambient dust and fluff". She relishes touching and shaping the wads of fluff - "cells, skin and hair" which she muses would be good insulation for a jacket to climb Everest in. This is where her idea of taking a relic from Rebecca comes in. She is going to take a feather from the jacket Rebecca wore to climb Everest, and use it in one of the works.

Rebecca is looking forward to seeing Cornelia's "painting". Sorry to disappoint, Rebecca, but Cornelia is a "new blood" young artist - she's a Turner Prize nominee. Paint? She doesn't use that - get real! Today's Contemporaries rarely resort to this outmoded means of expression. It's all about dead animals, elephant shit and immortalising everyone you've ever slept with. We're talking a legend in your living room, not a still life above the sofa. Cornelia is not going to get out there with her easel and her brushes - she's more into having garden sheds blown up by the Army then reassembling them in a new form. Not easy to live with - and try getting that up the stairs. (Although I heard someone at "Sensation" comment that Damien Hirst's sheep in formaldehyde - "Away From The Flock" - would make a stunning coffee table) But Rebecca does say she wants a "certain kind of experience", something "wacky" but "to be able to live with it". A tall order?

The series explores the symbiotic relationship of the artist and patron, one that we rarely see these days, when in most cases the artist and patron never meet. Purchasing a work of art from a gallery has a sort of P.O. Box anonymity - you choose it, you write your cheque, it is bubble-wrapped for you, you take it home, hang it on the wall, and probably only know that it was painted by a man or woman called X. You might have been given their CV, but no bonding has occurred - there is no part of you in the work you now own. But maybe that's a good thing.

When Cornelia Parker handed over one of the works she had made for Rebecca, I began to wonder whether you really want to play a part in the double- entry creative process. Cornelia had created earplugs made from the fluff she had collected from the Whispering Gallery at St Paul's. Clever? Yes. Yukky? Very.

I wonder what our Cilla would have made of their date. Will the lovely pair be seeing each other again? Will our Rebecca wear her fluffy earplugs? Tune in and find out how they enjoyed their date.

Date With An Artist

BBC 2, tonight, 7.30pm

Other artistic encounters in the series:

Peter Randall-Page meets deaf percussionist Evelyn Glennie. He wants to make a piece of sculpture which makes a musical sound when struck.

Chris Ofili, who makes paintings which incorporate big lumps of elephant dung, meets Anthony Ismond, a prisoner in Wormwood Scrubs. At the private view, fellow inmates give their views.

Jake and Dinos Chapman meet Justine Frischmann from Elastica (pictured below). She rejects their first offer to install a fibreglass wall with bleeding skulls in her bedroom. She'd prefer one of their notorious mannequins: "I'd rather be reminded of sex than death".

Julie Roberts meets a household of junior doctors in Glasgow. She is best known for her eerie paintings of medical ephemera. Dentists' chairs, straitjackets and gynaecological instruments are rendered in minute detail.

Andrew Gifford, a painter of landscapes with large, lowering skies as well as light installations using neon tubes, meets Dave Allen from Middlesbrough FC. Will Dave prefer the paintings or the more abstract light-box?

Catherine Yass, who specialises in photographic portraits which capture people's relationships with their environment, meets Mrs Leah French and Mr Charles Archer, two elderly Eastenders.