Attend a special evening hosted by Mike Atherton
Mr Clarke used the meeting to underline his stature as the most popular of the candidates among voters. He said the desire to win the next election should be the main consideration of members, and he was the man most likely to return the Conservatives to government.
Aides reported that Mr Clarke said the party should consider half men/half women shortlists when selecting candidates, adding that he was "driven to contemplate the idea".
If the party progressed at the rate it was going now it would take 60 or 70 years to get fair representation for women, and that was too long to wait, he said.
Mr Davis told the meeting that Tory wives made a bigger sacrifice than their MP husbands and got no public recognition for it.
Dr Fox said he was asked how the party could reconnect with women voters and how it could differentiate itself from Labour. He said the party must address "bread and butter" issues in a language voters understood, and proposed open primaries to ensure more women candidates were selected.
Mr Davis now has the declared backing of 67 MPs, with James Brokenshire coming out for him today. Mr Cameron won the backing today of Jacqui Lait and Robert Key, taking his declared support to 34.
Mr Clarke has the declared support of 23 MPs and Dr Fox appeared to trail on 16 - although his aides say that that will increase.
Tonight Mr Davis and Dr Fox will join the singer Shirley Bassey, Zulu leader Prince Mangosuthu Buthelezi, actress Joan Collins, novelist Frederick Forsyth, media tycoon Rupert Murdoch, composer Andrew Lloyd-Webber, lyricist Tim Rice, former US Defence Secretary Caspar Weinberger and the chef Marco Pierre White as Lady Thatcher's birthday guests.
Lady Thatcher's longtime aide, Cynthia Crawford, said that the former prime minister was looking forward to the party. "She cannot believe she is 80 and neither can I. She looks absolutely wonderful. I hope I look like that when I am 80."
In birthday messages, the outgoing Conservative leader Michael Howard said:"What (Winston) Churchill did in wartime, Margaret Thatcher did in peacetime. Her political will and her iron courage saw off the threats to our way of life that Britain faced in 1979. We all owe her an enormous debt."
Tony Benn, the retired Labour MP, paid tribute to his old political foe. He said:"Mrs Thatcher said what she meant and meant what she said. And did it. Although I thought the policies were catastrophic in terms of democracy, she did not do anything by deception."
Her former press secretary Bernard Ingham said:"The greatest tribute people pay these days is ’Come back Maggie’".
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