Mr Waldegrave, long regarded as a solid member of the pro-European wing of the government, exposed yet another fault line within the Cabinet when he said "the jury is still out" on whether Europe would become "impossible for us".
And in terms that Labour eagerly contrasted with John Major's memorable warning last month that those advocating life outside the EU were living in "cloud cuckoo land", Mr Waldegrave asserted that it was "not madness" to say Britain should be outside Europe.
In his remarks on BBC Television's Question Time, the Chief Secretary mused: "The nub is whether we are now finding issues which so grate on us in terms of our independence and our sovereignty that Europe becomes impossible for us. It is not madness to say we should be outside Europe. Of course, Britain could be outside Europe if it wanted to be. It is greatly to its interests to be in the European Union if it is the right kind of European Union."
Mr Waldegrave insisted last night that his remarks had been "taken out of context" and that he had made it clear that while it was "legally possible" to be outside the EU it was "greatly in our interests" to be inside.
Robin Cook, shadow Foreign Secretary, said the remarks were clear evidence of a fresh split and added: "No wonder we cannot get the beef ban lifted when John Major cannot get the Cabinet to toe the line.'
Mr Waldegrave had said on the programme that the Europe for which Britain had voted in the 1975 referendum - and in which the ultimate sovereignty would lie with the nation states - "can still exist". There were many in France and Germany who also thought like that. But he added: "If down the the line it became clear that there was an overwhelming consensus within the other countries of the present EU that they wanted to go for full Liberal Democrat federalism, then I think Britain is going to stand aside from that because I don't think we want that."
Kenneth Clarke had earlier reinforced his own strongly pro-European position by echoing the concerns of Jacques Santer, the European Commission president, about the xenophobic attitude of the British press. Mr Santer said: "I am very concerned at the anti-European mood - the same as I am about the anti-British attitude in the Continental press."
The Chancellor faces the uncomfortable prospect next week of having to veto EU measures to register Britain's protests at the beef ban. Some sceptics do not want the vetoing to stop until Britain has blocked progress on a single European currency. John Redwood, the former leadership challenger, told a meeting in North Shropshire: "We do not want those who brought us the Common Fisheries Policy and the Common Agricultural Policy bringing us a Common Economic Policy."Reuse content