Susannah Fiennes says she has read somewhere that the Prince of Wales likes his artist to look like artists. She certainly hopes so because he has invited her to travel with him to Hong Kong on the Royal Yacht Britannia for the handover ceremony, and she isn't used to dressing up.

Although she was surprised to be asked to record such a historic event (both the yacht and the colony are destined for new owners) Fiennes is not a novice recipient of royal patronage. Two years ago she accompanied Prince Charles on a trip to Oman, as his itinerant artist.  When the official duties were over they went into the desert and sat "at a discreet distance" from one another, each wrestling with their watercolours.  "It is a common interest. It's nice to have art as a meeting point. He's got the talent and he's got the concentration. I admire that a lot. You get the impression that, though time is limited, Prince Charles gets a lot of spiritual nourishment from his art."

At intervals, ice-cold drinks appeared on a tray. But Fiennes was not impressed by the desert, comparing it to a great gravel car park. "I ended up painting Prince Charles because there was just nothing else to paint."

As the only daughter of Lord Saye and Sele, Fiennes spent most of her childhood at the medieval Broughton Castle in Oxfordshire. After taking A-levels at Marlborough College, Fiennes (cousin of the actor Ralph Fiennes) went on to the Slade School of Fine Art. It was one of her contemporaries there, Emma Sargeant, who, as Prince Charles's former painter extraordinary, recommended Fiennes for the Oman tour. She thinks that a productive painting expedition to China - her prize as winner of the National Portrait Gallery's BP Travel Award in 1993 - may also have paved the way to Hong Kong.

Whereas Sargeant was already a well-publicised artist when Prince Charles "adopted" her, Fiennes, 36, has not had the same exposure and so has much more to gain from a royal appointment. "It is not a direct reflection of how good a painter you are, but it is helpful. It does lend a certain weight. People take notice."

Prince Charles funds his artists for the duration of their tour (June 27 to July 4 in the case of Hong Kong), and in return chooses whatever paintings he wants. The rest are the artist's to sell.

Fiennes's agreeably untidy studio in Clapham, south London, is full of images of China, especially of Chinese people on bicycles, gliding by as if in a frieze. On her easel is a large blurry oil painting of cyclists which she has just completed, obliterating layer upon layer of previous attempts at the same picture. "In the last few days, I've had a major breakthrough," she says.  "I just went for it. If you could X-ray that canvas you would see that I rework things a lot. I'm afraid to say that it's true of a portrait as well. It has become a bit of a sore point with some of the sitters."

If three years spent perfecting bicycles seems extravagant - "the geometry thrills me: I'm absolutely hooked on triangles" - think what four years must feel like to the Suffolk couple and their three young children who sat for the artist in 1993 and are growing old waiting for the picture.

"It's a saga," she sighs. "I could have given it to them after a week, but it wasn't what I wanted it to be. I've got photographs of about 50 different versions. It's almost a joke, it's so painful. The surface of the picture is like the moon, textured with lumps of paint. It tells a story.

"It's a sort of parody of a 17th-century composition of a family round a table - maybe Velasquez- and they gave me great freedom. Fortunately, I'm not that literal. It is a moment in history [said without irony]. When I'm ready to finish it, I could do it in a day. I've a funny feeling I'm nearly there."

Fiennes says she can work extremely fast when required. Some of her sketches in Oman were done on the move, of moving objects - "a little squiggle to suggest a palm tree, a little figure to represent scale" - and then worked up in her studio. Her recent portrait of Dame Fiona Caldicott, head of Somerville College, Oxford, was done at speed. Did she like it? "Well, she was wonderfully unvain."

Fiennes's main exhibitions have been at the Cadogan Contemporary Gallery in London (of Blackpool fairground attractions) and at The National Portrait Gallery (China). She thinks it is time that she came "out of the wilderness" and had another - of Oman and Hong Kong.

She looks at the old red rucksack that she superstitiously takes everywhere: at the brushes stuffed into a drum of barbecue-flavoured Pringles and very small battered palette. "Aren't I going to have to smarten up?" she asks.