A pleasing new routine has been added to my life in recent weeks. Every evening, I unfold my big map of America on the floor, hunch over it and search for some small town that I have invariably never heard of before. Then I take a pencil, mark a big fat cross and fold it back up again.

If I join the crosses, they are beginning to form a rather nice line, starting in New York and curving south-west through New Jersey, Pennsylvania and into Maryland. Within eight months, the line should stretch across the country from the East Coast to the West, covering a route of more than 4,000 miles.

The crosses represent my brother Phil Goddard, 47, and the ever-lengthening line marks his progress as he walks alone and unsupported across America in an extraordinary tribute to his late wife Jayne, who died of cancer in January, at the age of 49.

When he finishes, he will become one of an elite band of people who can say they have walked solo across the US, without any support crew or supply vehicle. The absence of a back-up team means that during the most isolated and physically demanding sections of the route, when shops and habitation are absent, he will have to push a heavy trolley loaded with food and water.

But this gruelling odyssey is his idea of a healing experience, an off-beat form of bereavement therapy by which he can make life without Jayne meaningful, rather than filling his days with the pain of her loss. It will also raise more than £10,000 in sponsorship for the Association for International Cancer Research.

“I thought a lot about how Jayne would have dealt with the situation if it had been me that died, and I thought she’d have tried to turn it into something positive,” he says.

“I hated just sitting in the house full of reminders of our 18 years together. Jayne and I went all over the world, and she was the perfect travelling companion, cheerful and uncomplaining. So I thought I’d do a really big journey in her memory.”

Phil is a freelance translator. My sister-in-law, who went by her maiden name of Jayne Comins, was one of the funniest, happiest, most hard-working people I know as she pursued two parallel careers — speech therapist and psychotherapist. She was one of Britain’s leading experts on the human voice, writing books and articles, making regular TV and radio appearances and lecturing all over the country.

“She knew a lot about her subject, but first and foremost she was an entertainer,” Phil says. “She made a huge impact on me and countless others. She had one of those sunny personalities that made people feel good.”

In June last year, she was found to have colon cancer, but the disease was already too advanced for there to be any hope of a cure. She died in St Thomas’ Hospital, London, on January 25.

“Jayne was surrounded by people she loved and she just gradually slipped away. Her room was almost on the top floor of the hospital and there was a spectacular view,” Phil recalls.

“The Thames kept flowing past, the London Eye kept rotating, and the trains kept pulling into and out of Waterloo station. All these things were going on normally outside, yet my wife had just died. That moment is etched in my mind.”

Yet since he began his walk in Times Square, New York, on June 25, he has disproved any notion that people aren’t touched by a stranger’s death.

Motorists wind down their windows and thrust money at him for the AICR, alerted to his cause by the profusion of publicity he has received from local newspapers, TV and radio stations along his route.

Café owners offer him free food, residents flag him down outside their homes and invite him in for a drink, people approach him out of the blue and offer him dinner or a bed for the night.

Before packing up his home in Blackheath, southeast London, and placing everything he owns into storage, apart from a rucksack full of clothes and a tent, Phil spent days poring over maps of the US to plan a route. But he concluded that making it up as he goes along, avoiding big cities and roads with more than one lane in each direction, is less constricting and far more enjoyable.

In Hancock, Maryland, he passed a chiropractor’s clinic with a hand-drawn sign in the window that caught his eye. As he stopped to take a photograph of it, the chiropractor came out and inquired what he was doing.

“So I told her about Jayne and about my walk and she just stepped forward and hugged me,” says Phil. “The five words on that sign summed up so perfectly why I’m doing what I’m doing — and why I’m not sitting at home wallowing in depression, or going round the twist with grief.

“It just said: ‘Walking is man’s best medicine’.”

You can sponsor Phil Goddard in aid of the Association for International Cancer Research at www.justgiving.com/uswalk and follow his progress at www.uswalk.blogspot.com