By Nick Assinder
Political correspondent, BBC News website
Tony Blair was already looking diplomatically isolated as he stood alongside George Bush refusing to call for an immediate ceasefire in the Lebanon.
Mrs Beckett's plea was reportedly rejected by Mr Blair
But it now seems he may be at loggerheads with his own Foreign Secretary, Margaret Beckett, after his officials rejected her officials' request for him to urge the president to call for such a ceasefire.
That split with one of his most senior ministers comes as he is said to be facing serious divisions within the Cabinet as well as amongst Labour MPs over his defiant support of the US line.
The BBC has learned that Mrs Beckett last week asked Mr Blair, through officials, to urge President Bush to call for an immediate ceasefire, but the suggestion was rejected.
She then asked for a halt to US military flights taking weapons to Israel stopping off in the UK - an issue she had already taken up with US Secretary of State Condoleezza Rice.
That call was also rejected, although the Foreign Office has now insisted that any such flights which stop in the UK only do so at US airbases.
It was already believed some ministers, including Environment Secretary David Miliband and International Development Secretary Hilary Benn, had reservations about the prime minister's stand.
Mr Blair and Mr Bush have the same position on the ceasefire
And former foreign secretary, Commons Leader Jack Straw had joined other Labour MPs in expressing serious concerns over the Israeli actions in the Lebanon and the prime minister's reaction to it.
They want the prime minister to call for an immediate ceasefire or, at least, agree Israel's actions in the Lebanon were "disproportionate".
It is now claimed that during last Thursday's cabinet meeting - around the same time Mrs Beckett was being overruled by the prime minister - one or more ministers passed notes to Mr Blair during the discussion on Israel telling him not to take their silence as consent for his policy.
And that is the problem for Tony Blair - it is looking like it is his policy rather than the government's or even the foreign secretary's, whose role he appears to have largely taken on.
There has been newspaper criticism of the way Mrs Beckett has handled the crisis, these latest claims will add to some people's belief that she is not wholeheatedly behind the policy she is defending.
For his part, Mr Blair has echoed the US view that ceasefire calls amount to commentary from the sidelines when what is really needed is to create the conditions under which the underlying causes of the violence can be addressed.
Opposition to US arms flights through UK
Mr Blair has said what is happening in Lebanon is a "catastrophe" and he says he wants an end to hostilities as soon as possible, that lasts.
Former environment minister Michael Meacher, a frequent Blair critic, said: "I do think that there is, to put it mildly, very widespread and deep unease about the failure to call unequivocally for a ceasefire, about the failure to condemn this catastrophic bombing of Lebanon as disproportionate.
"And beyond that, the seeming failure to appreciate that the longer this goes on, the more this will act as a breeding ground for terrorism, not only in the Middle East but throughout the world."
This is becoming increasingly serious for the prime minister at a time when his authority over his party has already been weakened by his looming retirement.