Sir Edward said on BBC Radio: 'We shall fight it with everything we have got to turn the tide of the recent by-election results. By the time we have the by-election, the economic situation will have improved and people will be able to see the results of John Major's policies, and that will help us in the campaign.'
The Tories are facing defeat in the Hampshire constituency, where Mr Milligan had a 17,702 majority over the Liberal Democrats in the 1992 general election. Although it would normally be seen as a safe Tory seat, it could be taken by the Liberal Democrats with a swing of less than 12 per cent.
Sir Edward's remarks underline the importance the Tory high command may now be attaching to defending the seat.
Mr Milligan's death has added to Mr Major's difficulties. The bizarre circumstances overshadowed the cut in interest rates yesterday.
One former Cabinet minister compared the mood in the Commons to the Profumo scandal, as the Government mounted a damage limitation exercise. 'There were all sorts of rumours and speculation and it was very unpleasant as it is now, and very sad,' Paul Channon, a former minister in the Thatcher government, said.
Senior Conservatives were anxious to avoid the Government being blown off course by a new sex scandal. Sir Norman Fowler, the party chairman, who spent two hours on Monday at Hammersmith police station after the body was found, played down its impact. 'Most people will take it for what it is, a personal tragedy,' he said. 'They will also take the view that it could happen in any political party or in any organisation.'
He prepared for Prime Minister's Question Time yesterday at a breakfast meeting at Downing Street with Chris Meyer, the No 10 press secretary. But the issue of Mr Milligan's death was said not to have been raised. John Biffen, a former Leader of the House, said the Government had had 'a lot of bad luck'. But Sir Edward Heath doubted whether all the Government's difficulties were the result of bad luck. 'What we have to do, all of us, is to work out where things do not work satisfactorily, and put them right,' he said.
The plight of the Tory party was frankly underlined yesterday when Kenneth Clarke, the Chancellor, said on BBC Radio that 'the fact is at the moment nobody's going to be a Conservative Prime Minister unless we can actually get the government into control and put it in a position where it has a reasonable prospect of winning the next election.'
Mr Clarke, answering a question about whether he saw himself leading the party, said he did not think the Conservatives could easily take another change of leader within three years. He said it would be an 'act of folly'.
Conservative Party activists last night gave their support to John Major when he began the first of his regional tours in Leicester.
'We are not in the least bit demoralised,' said John Brewin, chairman of the Stamford and Spalding Conservative constituency party. 'I don't think anybody is better than John Major when he is on the soapbox. He proved that in the general election and he did it again tonight.'
Although he did not resort to the soapbox at the city-centre hotel, he gave party workers a campaigning speech, explaining what he meant by 'back to basics' and raising the prospect of economic recovery. They emerged saying the Westminster sex scandals were diversions with no bearing on Tory support. It was the message Mr Major was longing to hear.