It is, officially, the first day of spring, but nobody has told the south of Dorset. Grey clouds are massing over the hills of Purbeck and a keen wind is blowing up from Bovington Camp. I am in a lay-by on King George V Road, once called Tank Park Road, staring intently at a tree and the memorial stone at its base. The inscription records that a famous man was fatally wounded at this site. This lonely hill hardly seems a fitting place for a hero to die.

I don’t normally seek out celebrity crash sites, but, having spent the past year writing about Lawrence of Arabia, I felt duty-bound to visit Clouds Hill, his cottage; and, a quarter of a mile away, this location, where, on May 13, 1935, the 46-year-old swerved his motorcycle to avoid two boys on bicycles and hit a tree. (The tree is no longer there: this one was planted in 1983 as a memorial by Tom Beaumont, who had been a gunner with Lawrence in the desert).

There is another stone, laid by the TE Lawrence Society, a little way into the woods. Both say he crashed somewhere “near” the respective memorial. Nothing in Lawrence’s life, not even the place where he was fatally injured, is entirely certain.

By this time, the gate to Clouds Hill, which now belongs to the National Trust, has been unlatched. It is the first day this year that the cottage has been open to the public, and business is brisk. It seems Lawrence of Arabia’s star refuses to dim. There is always something (David Lean’s centenary this year; a forthcoming auction of rare slides of Lawrence on the NorthWest Frontier) to keep the legend alive.

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Lawrence was ambivalent about his celebrity status; he happily used the influence it gave him when it suited him, but loathed the attention created by the stirring tale of an Englishman leading the Arab revolt (which, in fact, he didn’t). Hence his attempts to hide away in the services and at Clouds Hill.

“Don’t expect a palace,” he warned visitors, and the small worker’s cottage is far from what one might imagine as a home fit for a hero. When Lawrence rented it in 1923, for half a crown, he had enrolled in the Tank Corps under the name Shaw, having failed to conceal himself in the RAF as Ross. The cottage was his bolt hole while he was in the services; he used it to write and to recover from the strain of barracks life.

When he first saw it, Clouds Hill was derelict, crushed by rotten thatch and strangled by rhododendrons. Using money from his translation work - the early editions of his masterwork, Seven Pillars of Wisdom, were so lavish, they lost money - he tiled the roof and made the upper floors waterproof.

That is why the cottage is topsy-turvy, with Lawrence’s writing and music room (the gramophone, with a huge papier-mâché horn, is still in situ) on the first floor and the bedroom and library on the ground. It has a bathroom, but no lavatory. A man who had lived among the Bedu for almost two years had no need for such a modern convenience.

Quite how less robust visitors - including EM Forster and George Bernard Shaw - coped in these ascetic surroundings is another matter. Still, it was perfect for a man trying to escape his past. He retired permanently to the cottage in March 1935, hoping for “a life of Sundays”; two months later, he was dead.

THAT FIRST breath of spring has finally appeared, dappling the hills with weak sunshine, so I decide to visit the Lawrence grave at Moreton. This means driving through the dreary barracks of Bovington Camp - where Lawrence had ridden to send a telegram on that fateful day, and where he was taken after the accident (he died six days later) - and parking at the Tank Museum.

Opposite the museum, a two-mile footpath links Bovington with Moreton. This takes me through deciduous forest, showing the first bluebells, and gorse-studded heath - the latter a sliver of Thomas Hardy’s “Egdon Heath”, a description of which opens The Return of the Native. The author and the military man were great friends during the 1920s, and Lawrence frequently rode his Brough Superior motorcycle to Max Gate, the Hardys’ home in nearby Dorchester.

My first sight of the tiny village of Moreton is the elevated St Nicholas’s church. This is where the funeral was held on May 21, 1935. In the local tearoom, there is a Lawrence area, which has not only the hand-drawn bier his coffin was carried on, but pictures of the mourners, including Winston Churchill, General Wavell, Lady Astor and Siegfried Sassoon. The church suffered war damage - the Luftwaffe pilot must have been way off course - and its windows have been replaced not by stained glass, but by engraved panes, which flood the interior with a pure white light.

Lawrence is not buried at the church, but up the hill in a small, separate grave. It is a relatively simple affair for such an international figure, with his name on the headstone, the fact he was a Fellow of All Souls and a quotation from St John’s Gospel, Chapter 5, chosen by his missionary mother, a zealous Christian, which Lawrence was certainly not.

Back at the car, I drove off to see the last part of my Lawrence trail - his effigy, carved by his friend and admirer Eric Kennington. Life-size - it confirms Lawrence was 5ft 5in, considerably shorter than Peter O’Toole - it was intended for St Paul’s Cathedral, but ended up at the Anglo-Saxon St Martin’s church, in Wareham.

In the sculpture, the supine Lawrence is dressed in Arab robes, with his famous curved dagger clasped in his hand. His pillow is a camel’s saddle; his sandalled feet rest on a Hittite carving. Although Lawrence spent only a small fraction of his life in Arabia, and would doubtless have seen his legacy more in terms of the high-speed RAF rescue launches he helped to develop, the effigy perfectly captures the populist image of the fighting scholar and desert warrior.

In the centre of town is the small Wareham museum, which, like so many public buildings around these parts, has a Lawrence room. In it is a statement from one of the boys who were on the bicycles, adamant that the accident didn’t happen as shown in the movie (where they were pedalling towards Lawrence, rather than him coming up behind them) and that no mysterious black car (as some claimed) was involved. The fact is, accidents do happen. Even to heroes.

I finish my Lawrence trail at the Anglebury House restaurant. Next to the window seat is a small plaque announcing that TE Lawrence “spent many a pleasant hour drinking coffee in this seat”. As he never touched alcohol, I feel I can’t really raise a glass to the man, so I do what the uncrowned king of these parts would do: I order a large pot of coffee and watch the late-afternoon sunshine warm the streets of Wareham.

Robert Ryan’s novel about Lawrence of Arabia, Empire of Sand (Headline Review £12.99), is out now. To buy it for £11.69, inc p&p, call The Sunday Times BooksFirst on 0870 165 8585

Travel brief

What to see: Clouds Hill (01929 405616, www.nationaltrust.org.uk ), Thu-Sun, noon-5pm; £4, free to NT members. Moreton Tea Rooms (01929 463647), daily except Mon, 10am-5pm. Bovington Tank Museum (01929 405096, www.tankmuseum.org ), daily, 10am-5pm; £10, under16s £7; Lawrence exhibition on display from September. Wareham Town Museum (01929 553448, www.warehammuseum.fsnet.co.uk ), Mon-Sat, 10am-4pm; free. Anglebury House (01929 552988); closed Sun, Mon evenings. The slide auction is on Friday, Duke’s Auctioneers, Dorchester (01305 265080, www.dukes-auctions.com ).

Where to stay: Holmebridge House B&B (01929 550599, www.holmebridgehouse.co.uk ; doubles from £65), just outside Wareham, is run by Anita Saunders, whose mother’s cousin was one of the boys clipped by Lawrence. The Priory (01929 551666, www.theprioryhotel.co.uk ; doubles from £225, B&B) is on the river near the centre of Wareham.

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