Mr Santer, in Britain to promote monetary union and wider membership of the EU, said a single currency would bring economic benefits and he expected a large number of states would be in it from the start.
But Robin Cook said that it was unlikely Britain would sign up to be part of the project from 1 January 1999. A decision will be made by ministers around the end of the year.
"Tony Blair, Gordon Brown [the Chancellor] and myself, have all said it is unlikely that Britain will be joining, partly because we are a new government with a big agenda to do," he told BBC Radio.
But Mr Cook, regarded as a leading sceptic on the single currency in the Cabinet, left open the possibility of Britain joining at a later stage after the first wave. "I don't know about pretty soon after. We have always said that if it goes ahead and if it's a success, then in the longer term, it would be difficult for Britain to stay out," he said.
The Government is insisting on "genuine" economic convergence before Britain will join, and has promised a referendum.
The Tories, under William Hague, now rule out joining for the lifetime of the next Parliament - until 2007. The single currency issue split the Tories before the election, but some leading Euro-sceptics in the party will be pressing Mr Hague to go on the offensive to oppose Britain being drawn in at a later stage.Reuse content