The Chancellor refused to buckle, holding on through to the sweet course to his belief that Britain should preserve its option on joining a single European currency.
It is understood that Lady Thatcher tried to convince Mr Clarke that a shift of policy, ruling out Britain's entry into the first wave of a single currency, would help the Tories win the general election.
Allies of Mr Clarke said he privately believes it unlikely that Britain would be in the first wave of a single currency, but he refused to rule it out on the ground that a concession now would invite the Euro-sceptics to press for more.
"I would have liked to be a fly on the wall," said one source. "They had dinner just before Christmas. Ken's basic point is that the French may be fudging it, but if you give way now, there is no point where you can draw the line."
The Chancellor has never been afraid to speak his mind with Lady Thatcher. When she was forced to resign by the Cabinet, Mr Clarke was one of the first to tell her she should go.
Lady Thatcher's intervention came within days of the Chancellor's tense meeting with the Cabinet at which a number on the left of the party, including Stephen Dorrell, joined Euro-sceptics led by Michael Howard in challenging the Chancellor's paper on single currency convergence criteria.
Mr Clarke was forced into a partial retreat, and will return to the Cabinet with a new paper in the coming weeks. The Chancellor, however, secured the Cabinet's reaffirmation for the policy, preserving Britain's opt out on a single currency.
Last night friends of Mr Clarke remained adamant that there would be no change of policy, and dismissed reports that he was being forced into a corner by Mr Dorrell, and William Waldegrave, the intellectual leader of the left in the Cabinet, who has privately come down against a single currency.
Mr Waldegrave, the Treasury Chief Secretary, is said by some insiders to be highly influential in the shift towards the Euro-sceptics in the Cabinet. The next meeting of the Cabinet will be on 16 January.
Mr Clarke's paper will say that a judgement on whether other member states are fulfiling the Maastricht convergence criteria cannot be judged until the end of this year, making it impossible to justify a change of policy before the election.