"We live in a vibrant and connected world where together as a people we are strong. For our children and their children we should be facing the problems of the world together and not alone," said the 41-year-old former England captain in favour of Britain remaining within the 28-member economic bloc, the country's largest market.
His intervention two days ahead of the June 23 referendum is likely to help swing many of those still undecided voters.
Two separate surveys have put Remain ahead of the Brexit camp. An ORB poll for 'The Daily Telegraph' found that the Remain campaign attracted 53 per cent of definite voters while Leave had 46 per cent.
The poll showed an eight-point net reversal from last week, when Leave had a one-point lead among definite voters with 49 per cent of the vote compared to 48 per cent for Remain.
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According to 'The Financial Times', Curtice used new methodology recommended by an inquiry into why opinion polls had got their predictions of a hung Parliament so wrong in the 2015 general election.
"It is so close that any lead should be treated with caution," warned Curtis.
Indeed, a third survey by YouGov for 'The Times' gives Leave a 51 per cent lead compared to 49 per cent on the Remain side.
Cameron is all set to use the campaign's final 48 hours to hammer home warnings that Brexit would lead to higher supermarket bills and commuter fares.
He welcomed Beckham's support: "There was a very moving statement today from David Beckham talking about his children and saying how effectively, what he said to me was, 'You can't win in Europe, unless you're on the pitch'.