The news was given to a hushed Commons by the Prime Minister.
After reading a short Buckingham Palace statement, John Major told MPs: 'The decision to separate has no constitutional implications. The succession to the throne is unaffected by it. The children of the Prince and Princess retain their position in the line of succession and there is no reason why the Princess of Wales should not be crowned Queen in due course.'
This announcement, which caused a gasp of surprise among MPs, was made possible by the Palace's determination that the Princess, as mother to the second and third in line to the throne, should be kept in the fold.
The Princess is said to have considered the possibility of life outside the Royal Family - with the example of the Duchess of York, before her - and rejected it.
The summer has been a damaging one for the Royal Family. First there was the Duchess's relationship with a Texan businessman and then the publication of a taped telephone conversation purporting to be between the Princess of Wales and a man who said he loved her.
After their unhappy joint visit to Korea last month the Prince and Princess of Wales decided to go their separate ways - amicably, according to the Palace.
The timing of the statement, which came three days before the Princess Royal is to remarry, caused further speculation. Downing Street officials said the couple asked for it to be made before the weekend when their two sons would be returning from boarding school.
In a further sad irony, today marks the anniversary that Edward VIII signed a notice of abdication in 1936.
The Queen Mother said yesterday that she would, despite press reports to the contrary, attend her grand-daughter's wedding in Scotland to Commander Timothy Laurence.
The Prime Minister spoke to the Prince and Princess of Wales separately in the past week. He was forced to postpone an important meeting with Jacques Delors, the President of the European Commission, after being told by Buckingham Palace that the statement would be issued yesterday afternoon.
Mr Major told the Commons: 'I am sure that I speak for the whole House - and millions beyond it - in offering our support to both the Prince and Princess of Wales. I am also sure that the House will sympathise with the wish that they should both be afforded a degree of privacy.'
His appeal was strongly supported by all sides, and the reporting of events leading to the separation seems certain to increase pressure for a press privacy law.
The Bishop of St Albans, the Right Rev John Taylor, said the separation was 'a body blow' to the life of the nation. 'But the Church has lived for long enough with the principle that each of its members is human and frail, so that most people will want to be sympathetic,' he said.
The Princess of Wales will move permanently into apartments at Kensington Palace, while the Prince remains at Highgrove, in Gloucestershire. When in London, he will stay at Clarence House.
The Princes William, 10, and Harry, eight, are pupils at Ludgrave boarding school near Wokingham, Berkshire, so the question of their permanent residence has yet to arise. They will split holidays equally between their parents.
The Prince and Princess intend to remain married, according to the Palace. Their lives will be separate and formalised, but they will occasionally attend functions and ceremonies together. There are plans for them to dine together tomorrow on the royal yacht Britannia during the European summit meeting in Edinburgh. It is understood there has been no formal financial settlement or maintenance agreement, but Palace officials said the Prince intends to provide for his family under current arrangements, with funds coming from the Duchy of Cornwall, not the Civil List.
The Princess intends to continue with a full diary of public engagements organised by the couple's joint staff at St James's Palace, although the split will lead to some extra appointments, at the Prince's expense.
Despite the Palace's insistence that neither party had any intention of divorcing, the Archbishop of York, Dr John Habgood, issued a statement on behalf of himself and the Archbishop of Canterbury, Dr George Carey, which said the Prince's position as Supreme Governor of the Church of England would not be affected if Charles were to divorce Diana.
The Princess of Wales will become Queen on Charles's accession - again, the Palace insisted there are no plans for Charles to step aside in favour of his elder son - but reports from inside the Palace that the Princess would attend the Coronation were received with scepticism.
'The Sovereign is the Supreme Governor of the Church of England and the Coronation is a religious ceremony,' said Vernon Bogdanor, Reader in Government at Oxford University. 'Would it be appropriate in those circumstances to take those vows when you are formally separated?'
At Westminster, the separation announcement was met with sadness, but failed to end speculation on the succession. Last night MPs on all sides of the House, including some close to the Prince, said privately there were 'profound' constitutional issues. Some said the monarchy, while not imperiled, may be at a watershed.
Loyal Conservative MPs privately said Mr Major's remark that Diana could become Queen although separated was 'untenable' and some ministers questioned Mr Major's judgement for adding it to his statement. 'It's buying time, but frankly it's inconceivable that we could have a King and Queen who are separated,' said one senior Tory MP. Many, despite Palace denials, expect the couple to divorce in time.
Some monarchist Tory MPs agreed with the republican Labour rebel, Dennis Skinner, that the Royal Family had been 'demystified'. Patrick Cormack, Tory MP for Staffordshire South, said: 'You can become too matey. Things like It's a Knock Out and the Royal Family participating in that do not help. If you have a monarchy, it is important they are seen to be different.'
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