Last autumn Malcolm Rifkind, the Secretary of State for Defence, appointed him a personal adviser. And now he has been asked to help the Ministry of Defence solve one of the most serious financial problems it has so far encountered.
There is no doubt that the Eton-educated multi-millionaire had more than a passing influence on Mrs Thatcher when she was prime minister; nor that her fall marked a serious setback for him. John Major has little sympathy for his brand of radical conservatism. But Mr Hart, 50, has friends in Mr Major's government and it is through them that he has remained a figure of real influence. This is how he seems to prefer it: sitting on the edge of the political world, pulling strings.
He is closest to Michael Portillo, whom he has known for 20 years. Earlier this year, it emerged that Mr Hart was involved with two young radicals who planned to set up a 'think-tank' with the sole purpose, it seemed, of promoting Mr Portillo as future leader of the party. Mr Portillo denied he was involved. But there was a leaked memo written by the two activists, and addressed to him, which explained that the 'think-tank' would do its best to look independent and would be careful not to identify him as its focal point. It is said that Mr Hart helped Mr Portillo write his speech to the Tory party conference last year.
Mr Hart is close to several other Cabinet ministers, and former Cabinet ministers, including Norman Lamont. But his friendship with Malcolm Rifkind, which has been the key to his public re- emergence, is difficult to understand. Ideologically, the two men seem to have little in common.
Mr Hart has some aptitude for defence - it is understood that Baroness Thatcher would consult him particularly on defence matters. His original appointment by Mr Rifkind horrified military leaders: they prepared themselves for a vigorous assault on their spending, which has duly followed. There are grounds for believing that Mr Hart has been the driving force behind current defence cuts.