LORD OAKSEY begins by saying, 'I'm not sure I can bear to confess this.' Then he takes a breath and goes on to describe the day Jacko died. Bear in mind that Jacko was a dog. Some would say 'only' a dog, but that's not the point; the emotion is real.

Jacko was a black and tan terrier who lived with the racing commentator for 13 years, then died 12 months ago, leaving a sad corpse where once there was a puppy and companion who slept on his master's bed. So here is the problem: what do you do when your pet dies? Physically. With the body.

Lord Oaksey, sitting in his Wiltshire home with another dog on his lap, lays out the detail. 'Jacko died of a heart attack. I was away and travelling back, talking on the telephone to my wife, and she told me that she'd got the vet to come and take him. Yes, I probably did stop the car and, yes, I think I cried.'

He stops. Goes on: 'So when I came back he was at the vet's and he had, in fact, died. It was horrid, and what revolted me was that we took him in a sort of plastic bag and buried him in a place where I have buried dogs before, in our garden, under a tree - a perfectly nice place. But I woke up that night revolted by the whole idea of him being eaten by worms and going bad. So, early next morning, I dug him up and burnt him. It wasn't easy. I managed it on a great big bonfire. It really made more of a nightmare of the whole thing, but I think cremation is better.'

He concludes: 'Actually, I would have quite liked to have had a gravestone for Jacko but I haven't got one. He's not at this moment, so to speak, commemorated, except by photograph. I have some very good photographs of him . . .'

That is the end of Lord Oaksey's story and what it says is this: society is beginning to come to terms with the fact that animal loss can be moving, and even tragic. The RSPCA, for instance, has just published a pamphlet on easing bereavement at pet loss; there are a growing number of grief counsellors who are trained to help. But grief is one thing. Disposal of the remains is another.

As Lord Oaksey found to his emotional cost, the apparently simple task of getting rid of your pet's body can be a delicate matter, conjuring up nightmares of apparent brutality or, at best, indifference. What do you do?

Traditionally, you either leave the corpse with a vet, who will almost certainly have the body cremated by a specialist company, or you find a quiet corner of the garden and dig a hole - and maybe have a cry when no one is looking.

For many of the 50 per cent of British householders who own a pet, however, this is no longer enough. People are seeking personalised alternatives to blunter options, and a small industry is growing up to meet the demand.

In Winchfield, Hampshire, it happened by chance. Carole and Barry Spurgeon discovered a large, ivy-covered lump in their back garden and, stripping away the fronds, found an ancient brick kiln. When Barry, a fashion agent, suggested people might pay to have their dead pets cremated there his wife laughed. Now she helps run Dignity, a service that began last August and arranges an average of one daily cremation.

'A hundred years ago, most animals were working animals and lived outside,' says Mrs Spurgeon. 'Nowadays, animals are so much a part of the family. People can grieve far more for a cat than for some uncle they hardly ever see.'

The service includes collection, incineration and return of the ashes in an urn, usually with dried flowers as a gesture of sympathy. Basic costs range from pounds 50 for a cat, to around pounds 100 for the biggest type of dog. A rabbit, a hamster and a goat have also gone through Dignity's incinerator. It's tempting to snigger, but Mrs Spurgeon is having none of it.

'People cry,' she says. 'They need to talk sometimes, too. They like to tell you about their pet's life, when it was a puppy, how lovely it was, the things it did.'

On a shelf in Carole Spurgeon's house is a pot with a German shepherd dog's ashes inside - all that remains of the family pet who died last year: 'He was sitting in his pot in the kitchen at first,' says Carole, 'and we would say 'Morning, Brutus' when we came in. Now he's been moved to the hall. It's nice. We know he's in there.'

In Birmingham, there is a private pet cemetery run on land owned by the RSPCA where 300 animals have been laid to rest at costs of up to pounds 500 each, including memorials. Here, sometimes, an Asian lady appears with a tape recorder, stands over the grave of her dog and plays music he once loved.

Pat Harris, an RSPCA branch secretary, points out that many owners make use of the 'chapel of rest' for a last look at their pets before burial. Others bury their pets with toys and food, and at Christmas the place is covered with wreaths. There are dogs, cats, birds and a hamster buried here.

Sadder than that, however, is a story from Newbury Lodge Pet Cemetery, near Andover, Hampshire, which Janet Webb runs with her husband, Ron, to fund a dog rescue service. 'One man buried his alsatian, and was so upset he used to come and sit by the grave in the dark sometimes,' Mrs Webb says. 'He would sit there for 10 minutes and put flowers on the grave. Then he became worried that we might have burnt the dog and he wanted us to dig him up. We said, 'Look, your dog is there, the head is pointing up the road; he has a little coffin . . .' '

Customers pay pounds 100 for a small plot with a headstone at Newbury Lodge, and 90 people have buried their pets there. Some owners have no garden; some are worried about abandoning their loved creature to a vet (they tell stories of skinned corpses and dog meat); others take the long-term view that home burial is only OK as long as they stay in that house - new owners might dig up the garden and disturb Ben, or Spot, or Fido.

People do not forget their pets. Lady Oaksey says she doubts that a year has been long enough for her husband to get over Jacko's death. Lord Oaksey thinks a gravestone might have been a good idea. They last, you see.

In Bognor Regis, West Sussex, Penny Keen, a partner in a masonry firm, has set up a separate business, Petstones, making memorials for animals out of marble, granite and slate. She did it because people kept asking. 'They would say, 'I know this sounds silly but . . .',' she says. And it probably does when you read some of the inscriptions: 'Bonnie, you will always walk beside me', or, 'Simply the best'.

But five or six people a month pay an average of pounds 100 each to commemorate their pets with precisely this sort of message and Ms Keen knows of children who were unable to accept the death of their dog or cat until asked to think of an inscription. This focal point for bereavement, she says, can have a liberating effect.

Maybe this is the point, not just for children but for adults, too. A grave, an urn, a stone, a tribute can provide the emotional release people need.

Certainly, the subject is being taken increasingly seriously by academics and animal professionals. Peter Davies, director general of the RSPCA, is considering further moves into the business of pet bereavement - 'There seems to be an increasing demand,' he says - and in July the Society for Companion Animal Studies will run a residential seminar at the University of Liverpool. The subject? 'Pet Loss and Support for Bereaved Owners.'

Should we laugh?

(Photographs omitted)