Beckham, sporting a silky white, loose-fitting tracksuit with gold flashes, was surrounded by local TV crews and photographers as he toured a UK-Singapore sports science exhibition.
He looked on in silence as exhibitors explained their stands, demonstrating new ways of tackling sports injuries, aerodynamics and the theory of how soccer stars could "bend it like Beckham" from free kicks.
The Real Madrid star appeared to take a keen interest in an experimental "Resprivest", designed by researchers at Loughborough University.
It is worn underneath sport shirts and aims to boost performance.
Mr Blair and Beckham also met youngsters from local schools taking an active interest in the science of sport.
Mr Blair signed a science co-operation agreement with the Singapore government yesterday.
The Prime Minister's wife Cherie toured the Singapore Science Centre separately and expressed confidence in the London bid.
"We are doing fantastically well," she said.
Wearing a matching grey mid-length coat and dress ensemble with ivory lapels, she presented a science prize to a local schoolgirl - and on hearing the youngster wanted to study in Britain, suggested she apply to London's Imperial College.
Mrs Blair met researchers from Sheffield University who demonstrated models showing the aerodynamics of sport, including how Wimbledon stars achieve their favourite tennis shots.