Lady Thatcher has already told friends that she admires Mr Blair's disciplined determination. She was reported in the Daily Mail last September saying: "He knows exactly what he wants and how to go about achieving it."
Mr Blair, for his part, has put his respect for Lady Thatcher's leadership qualities on record. He wants to create a new politics, in which talented and experienced people of all views are welcomed into government, regardless of their views.
Labour advisers emphasise that Washington is deemed the perfect post, because the former Tory prime minister cuts a formidable figure in American political circles.
She is regarded almost reverentially by the Capitol Hill elite, as well as academic and business folk across the US.
The understanding has been brokered by one of the Washington embassy's former rising stars, Jonathan Powell, who left the diplomatic service to become an aide to Mr Blair. Mr Powell is a younger brother of Sir Charles Powell, Lady Thatcher's former foreign- policy adviser.
The growing bond between the Blair and Thatcher camps has been aided by the close friendship between Carla, Sir Charles's Italian wife, and Peter Mandelson, Mr Blair's Machiavellian aide: the pair are often seen on each other's arms at soirees.
Lady Thatcher will take over from Sir John Kerr, who, it was announced in February, will return to London later this year to head the Diplomatic Service. A decision on the Washington ambassadorship, the most sought- after Foreign Office posting, was to be delayed until after the election. But sources say that the US administration has been sounded out unofficially, and that President Clinton is "more than happy" with the appointment.
If the posting is confirmed, Lady Thatcher will enjoy the comforts of a magnificent Lutyens residence on Massachusetts Avenue, described as the "second-nicest house in Washington", with its white colonnade, footmen, white and gold Minton china decorated with the Royal cypher, and up to pounds 14m a year running costs.
Sir Denis Thatcher has already made one "reconnaissance" trip to scout out which of Washington's exclusive country clubs will become his golfing venue. He will find President Clinton a keen partner on the greens. At an auction in aid of his daughter's school last year there was fierce bidding for the President's offer of 18 holes with himself at the Army- Navy Country Club.
As one source close to Mr Blair put it last night: "Who cares what she did to Britain? What matters now is whether she'll help us win Basildon."Reuse content