Aides to the Prime Minister voiced optimism that the Queen's courtiers and staff had learned from the close co-operation with New Labour, and that the process might continue.
Pressure for reform of the monarchy is mounting. Labour MPs are now openly calling for a "more open and accessible Royal Family" and closer links with the Blair administration.
It is also being suggested that Blairite reforms of the House of Lords will open up the enclosed world of the court to a wider spectrum of modern life, as Labour has done with the Treasury.
John McWilliam MP, chairman of Labour's Parliamentary Affairs Committee and an expert on constitutional issues, said yesterday : "It is clear there is a far better relationship between Number 10 and the Palace than there has been for a very long time indeed. Out of this might come a more relaxed and open monarchy.
"The changes between 1936, when a king was forced to abdicate for wanting to marry a divorcee, and now are very dramatically underlined by the almost- state funeral of Princess Diana. It would therefore be wrong to suggest that the trappings and organisation of the monarchy are immutable."
He contrasted the monarchy with the newly reconstituted Spanish royal family of King Juan Carlos, and the model of "very successful" democratic Scandinavian monarchs.
I think the people want a more open, accessible monarchy, and one that appears to be more in tune with modern life," said Mr McWilliam. "That is not to suggest that the Queen doesn't know what is going on. She knows extremely well. She is the most experienced politician in the world, in the constitutional sense. But she is hidebound by Victorian protocol that didn't shatter - but got some huge cracks - last week."
Labour's plans for reform of the House of Lords, robbing hereditary peers of their right to vote in the upper chamber, could lead to the Queen's courtiers being drawn from a wider circle than the peerage and the top echelons of the armed forces, he added.
Roger Stott, a senior Labour back-bencher, said : "It is clear that the Prime Minister has been very touched by this tragedy and has been in close touch with Prince Charles in particular.
"We very much hope that this relationship will mature into a new and deeper understanding on the role of the monarchy between the Royal Family and the elected government of this country.
"I am sure that every person in this country would wish that Princess Diana's influence on Prince Harry will not be subjugated by the stuffy and old-fashioned views currently prevailing within the Royal Family." By contrast with Tony Blair's "sensitive touch on the tiller", they had not been as responsive to Diana's death as the people expected, he added, "probably because of ancient protocols regarding how they should react.
"Now is the time, before we reach the new millennium, to have a new understanding of the way in which the Royal Family operates in the future."
The Commons Select Committee on Culture, which is to look into the issue of media harassment of the Royal Family, is likely also to consider the wider issue of protocol. Some MPs want the Queen to be freer to speak her mind and show her feelings.
There is scant appetite at Westminster for republican solutions. "I am personally still convinced that there are safeguards in the constitutional monarchy that an elected head of state just would not possess."Reuse content