Novelist Grace Wynne-Jones jumps at the chance to take a haughty llama for a stroll in Ashdown Forest Park.

'Walking With Llamas," proclaimed the brochure in a Sussex library. "You can now take a llama for a relaxing walk in acres of unspoilt private grounds."

Some days later I walk up the Ashdown Forest Llama Park's curving driveway. The spacious visitors' centre includes a cafe and large shop selling alpaca knitwear and South American handcrafts and a "World Of Wool" museum. Entrance to the visitors' centre is free but I have to pay £20 (€29.93) for the walk.

The park has more than 80 llamas but only some of them have the calm temperament required for llama-walking and many are kept for breeding. A good quality llama can fetch £2,000 (€2,935). Linda Johnson, the park's owner, started keeping llamas as a hobby but then decided to share their special allure with the public.

Llamas are members of the camel family and every one is different, Linda says, "They need routine. They are very superior, almost haughty, but also gentle and unassuming." My fellow walkers are all pleasant middle-aged couples. Some have been given the walk as birthday presents. Sharron Murfin, one of the park's managers, is our leader.

The llamas are led from their enclosure. Each one is wearing a colourful halter. I stare at their luxuriant eyelashes, their long elegant necks, banana-shaped ears and huge shiny dark eyes. Their mouths seem perpetually curved into a slight smile. In Peru, they are frequently used as pack-animals. They walk with an elegant, leisurely gait. Sharron tells us that llamas are sometimes used for guarding sheep because they don't like foxes or dogs.

Llamas can be black, white or brown or an exuberant mixture of various colours. My llama is white and his name is Frostie. Llamas can live for 16 years, and sometimes longer. Frostie is five, but was "born middle-aged", Sharron says. He is the veteran of the group.

Frostie accompanies me patiently, almost stoically. We have all been given small bags of carrots. I offer one and he stops and crunches it enthusiastically. He had once won Best Male Castrated Llama at a local show. He is now slightly plump.

The park's llamas are occasionally used as extras on TV and videos. Frostie has appeared on the TV series What The Romans Did For Us. On another occasion a dentist was filmed walking through a herd of llamas for a training video, though the park's staff could never figure out why this particular shot was required.

Frostie is a llama with attitude. When we pass some non-castrated male llamas, most other llamas lift their tails to signal their submission, but Frostie's tail doesn't budge. When I pat his neck he lingers a while to savour the experience.

The other llamas in our group are named Barney, Pedro, Toby, Felix and Leroy. Sharron tells us that Leroy is always a bit tousled and dirty. He seems like a leggy teenager. Pedro is being led by a member of staff. "He didn't get a good start in life but is calmer these days," Sharron explains. Felix was "frisky". Sometimes Toby, who "prefers men", stops and suddenly strikes a pose, as if vainly waiting to be photographed.

All the llamas like wandering into the ferns that border the pathway. They clearly like the feel of the thick leaves. I get the impression that women walkers were making slightly more of an effort to bond with their llamas but everybody seems to be enjoying themselves.

The walk lasts for about one and a half hours. We lead the llamas back to their enclosure, say goodbye to them and then Sharon offers each of us a keyring with a picture of a llama on it. "Thanks Frostie," I say, giving him the remainder of the carrots.

We go indoors and I sit in the cafe with a couple called Chris and Rosie who have also been on the walk.

This kind of thing is not new to them. They have recently been on a camel trek in north Somerset to celebrate Rosie's 50th birthday. They have enjoyed the llama walk and I say I have too. Though Frostie is still a stranger to me in many ways, I have enjoyed his exotic and calming company.

And the cafe's llama-shaped biscuits are very good, too.

The Truth Club by Grace Wynne-Jones is published by Tivoli, €9.99. The park's website address is www.llamapark.co.uk