As Wikipedia explains; The movie was filmed in Trinidad and Tobago allowing [director John] Huston and Fox to use blocked funds in the UK, receive British film finance and qualify for the Eady Levy. Clicking on that last one gets some details. The levy was a tax on the movie-going public, added to the box office ticket price, with half the amount rebated to the exhibitors of the film, and half to the producers of British films.
And, to be a British film--and qualify for the lucrative subsidies--it had to be shot in Britain or the Commonwealth, and having only three non-British actors, directors and technicians. Or so says Wikipedia. Now, for the rest of the story we turn to Jonathan Stubbs' The Eady Levy: A Runaway Bribe? Hollywood Production and British Subsidy in the Early 1960s;
...the Eady levy encouraged Hollywood companies to use their British subsidiaries to produce films which actually offered representations of Britain [or British experiences overseas], thus further complicating the distinction between British and American film-making.It also encouraged some creative accounting schemes to hide the true origin of films like the blockbuster Lawrence of Arabia. The movie moguls had to convince the British Board of Trade that the film met the criteria to qualify as British. Which wasn't easy for a film that was financed by an American like Sam Spiegel using the resources of Columbia Pictures, even though technically the producer of the film was Horizon Pictures (GB) Ltd, which Spiegel founded in 1952.
As the Board of Trade was aware, Columbia paid the salaries of many of the people involved in the making of Lawrence and then loaned them out to Horizon Pictures. As a member of the BoT put it, 'this engaging of staff by a foreign company...even though loaned or assigned to a British company, seems to me to be pretty close to direct participation by a foreign company.'
Further, the film's 202 minute running time was comprised of exactly 40 seconds shot in British film studios--Shepperton, and Goldhawk, Shepherds Bush--and 3 minutes, 2 seconds on locations on British soil. The bulk of the film was shot in (then dirt-poor) Spain (116 minutes) and Jordan (65 minutes).
But the Brits are nothing if not stiff upper lipped, so the BoT ruled that, 'there is no doubt that this film is essentially British in the light of the rather wider interpretation which...we allow to American sponsored films'. Which settled matters. Until Lawrence was entered in the Acapulco Film Festival in 1963...as an American film.
Which required a re-evaluation of the BoT's earlier decision to classify it as British. But, millions of dollars of investment by Hollywood was at stake, so the Board was up to the task of re-affirming Lawrence as a product of the Empire. It was decided that the Mexicans who'd classified it as an American film were in error. And when it won the first prize in the festival, the honor of accepting it went to the British Ambassador to Mexico.
Whew! The coast was clear again. So clear that in 1969 another American film officially registered as British, Stanley Kubrick's 2001: A Space Odyssey, was able to compete in the Moscow Film Festival as the official American entry. Again, the British film board took it like her majesty's men they were.
Other films labeled as British--and collecting subsidies from the British taxpayers--were, over the years of the Eady Levy; The Bridge on the River Kwai, The Guns of Navarone, Tom Jones, Treasure Island, The African Queen, Captain Horatio Hornblower and Ivanhoe.