The Prime Minister sought to patch up the differences after he had failed to give his support to Mr Clarke in the Commons.
Mr Clarke has told colleagues that he is determined not to allow the Euro-sceptics to push the Cabinet into closing the option of a single currency. He is confident that he has achieved that.
Relations between the Chancellor and the Prime Minister could be stretched to breaking point over the drafting of the manifesto commitment on Europe.
Senior party sources have said it cannot be left to the foreign policy manifesto review group under Douglas Hurd, the Foreign Secretary, and will have to be decided by key Cabinet ministers.
Mr Clarke is opposed to a referendum but there are signs that Mr Major may seek to reassure the Euro-sceptics by hinting at a referendum in the manifesto to deal with the constitutional issues which he believes would be raised by a single currency.
The pressure for a referendum will be stepped up today by Teresa Gorman, one of the whipless Tory MPs, when she publishes a Private Member's Bill proposing a referendum. The resignation of the Chancellor would plunge the Tories into a crisis which would almost certainly destroy any hope of holding on to power at the next election. But the fact that it is seen by Cabinet colleagues as a possibility, underlines the danger facing the Government over its divisions on the approach to a single currency.
"Ken's behaviour has been incredible. We know where it leads. We have seen it happen twice before," said the Cabinet source. "If there had been a sacking before now, perhaps none of this would have happened."
Baroness Thatcher's downfall began with Nigel Lawson's resignation as Chancellor. Norman Lamont has become Mr Major's sharpest critic since resigning as his Chancellor. Yesterday, Mr Lamont said: "At some point we have actually got to confront the arguments as an issue of principle." Mr Lamont said on BBC TV's On the Record that he had changed the Maastricht Treaty, against the advice of Mr Major and Mr Hurd, to prevent Britain being legally bound to re-enter the exchange rate mechanism.
"I refused to accept that membership of the ERM ought to be a legal obligation. If I had not deleted that by my own personal action from the treaty, we would today be absolutely committed to rejoining it."
He also revealed that he had disagreed with Mr Clarke in Cabinet over the harmonisation of value-added tax in Europe. "Kenneth Clarke and I actually disagreed about this at the time. I remember I told him that I didn't intend to go along with the harmonisation of indirect taxes in Europe."
Mr Lamont said that Sir Edward Heath, the former prime minister, was among the politicians who believed in European political integration - "the sooner Westminster becomes a county council, the better". Sir Edward dismissed his remarks as "claptrap".
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