The deal, involving more than pounds 20bn in sales of Tornado fighter-bombers and naval vessels, is believed to have been the largest in history, and the money Mark Thatcher is said to have made from helping to broker it - allegedly pounds 12m - would explain his sudden rise to conspicuous wealth.
If the allegations are proved, Baroness Thatcher's position will be, at the very least, gravely embarrassing because such a clash of public and family interests would appear to be very much at odds with accepted procedure for ministers, not least the head of the government.
The allegations will electrify the Conservative Party conference in Bournemouth, where Lady Thatcher is to attend the opening day on Tuesday. Sources close to her said she would not be making any comment until she had studied the allegations in detail.
Last night, Tam Dalyell, MP for Linlithgow, who has previously accused Mark Thatcher of benefiting hugely from Al-Yamamah, promised to raise the issue in Parliament again as soon as MPs returned to Westminster next week.
In November 1992 Mr Dalyell asked the Government to confirm or deny that 'Mark Thatcher received approximately pounds 10m soon after the signing of the memorandum of understanding for the Al- Yamamah deal in September 1985, and that the agreement on the deal specified that he would receive a further pounds 10m subsequently'.
'As soon as the House of Commons comes back, I will return to the questions I put and ask what the state of knowledge was at that time - and what it is now,' he said. 'And this time we must have some answers.'
The new allegations, in today's Sunday Times, are supported, the paper says, by transcripts of tape recordings made by Saudi intelligence agents while monitoring rival bids by Britain, France and the United States to supply the Saudis with arms.
The tapes were leaked to it by Mohammed Khiweli, the Saudi first secretary to the United Nations, who defected in May and was granted political asylum by the United States. The central new allegation is that Mark Thatcher was the indispensable contact to Lady Thatcher for the man who eventually secured the Saudi deal for British defence companies, who is named as Wafic Said, a Syrian millionaire.
Adnan Khashoggi, the international arms dealer, is quoted directly by the paper as saying: 'Wafic was using Mark's intelligence. His value to Wafic was his name, of course, and whenever Wafic needed a question answered Mark would go directly to his mother for the answer.'
The paper claims that British Aerospace executives involved in the deal at the time have confirmed Mark Thatcher's involvement, and the alleged pounds 12m commission he received. The total commission for middlemen on the deal, it says, was a remarkable pounds 240m.
In a further allegation considerably damaging to Lady Thatcher herself, the paper claims the permament secretary at the Ministry of Defence, Sir Clive Whitmore, was sent to the then prime minister to deliver what was termed a 'witch's warning' about the potentially disastrous consequences of her son's involvement. Mrs Thatcher, however, apparently ignored it, the paper says.
The Al-Yamamah arms deal was investigated by the head of the National Audit Office, Sir John Bourn, but the House of Commons Public Accounts Committee declined to publish his report after its chairman, the Labour MP Robert Sheldon, had held secert talks with the Ministry of Defence. The MoD invoked arguments of national security to veto publication of the report.
Defending the decision not to publish, Mr Sheldon said there had been 'no evidence of fraud or corruption'. However, Dr Kim Howells, a member of the PAC at the time, said last night: 'There were allegations flying about all over the place and they specifically included allegations that Mark Thatcher had been one of the main middlemen in the whole deal, and there was a hint that his mother had paved the way for him.'
He added: 'I can believe it. Everyone said if he was not the major middleman, that he was set to make more out of it than any other British middlemen.'
Mark Thatcher's business interests, as opposed to his ill- starred motor racing ambitions, first caught the public eye when he began promoting Japanese textiles in Britain. Real scandal was first associated with his name when, in 1981, his mother persuaded the government of Oman to give a pounds 300m contract to the British construction company Cementation, for which Mark was then acting as an intermediary. When the story broke in 1984, Mrs Thatcher refused to comment on her son's role, insisting instead that she had 'batted for Britain'.
The younger Thatcher subsequently moved to the United States. Now 41, he lives in Dallas with his Texan wife, Diane, and their two children. He is widely known for expensive tastes, enjoying sports cars, air travel with his butler in tow, and grand hotels.
Mr Dalyell's claim that he made huge profits from the Al- Yamamah contract was repeated last year by Howard Teicher, a Middle East expert on Ronald Reagan's National Security Council in the 1980s.
Mr Teicher said: 'I read of Mark Thatcher's involvement in this arms deal in dispatches from our embassy in Saudi Arabia, from intelligence reports that were gleaned in Saudi Arabia and Europe and in diplomatic dispatches from other European capitals. I considered these dispatches totally reliable, totally accurate.'
'I did not think that people would loosely accuse the son of the Prime Minister of being involved in such a transaction unless they were certain it was the case, and the fact that I saw his name appear in a number of different sourced documents convinced me of the authenticity of at least the basic involvement on Mark Thatcher's part. He was clearly playing some kind of role to help facilitate the completion of a transaction between the two governments.'