"In an information age of fast, swift communications, modern political parties cannot continue to survive in government if they are disunited or carry major weaknesses," says the memo, which has been passed to The Independent.
Officials at Millbank said there was strong pressure from grassroots party members for an end to the feuding between allies of Mr Blair and the Chancellor, Gordon Brown, which has been blamed for the resignations of Peter Mandelson, Geoffrey Robinson and Charlie Whelan, Mr Brown's press secretary.
One Labour source said: "I am sure the entire Cabinet has got the message now. We now have an opportunity to move forward and concentrate on delivering our promises."
Labour's private opinion polling shows the Tories are still seen as more divided than Labour. One reason for this is that Mr Blair is seen as a much stronger leader than William Hague. However, Labour officials are alarmed by a sharp increase since last summer in the number of voters who regard the Government as "sleazy" and "arrogant" - a trend they expect to continue since the revelation of Mr Mandelson's pounds 373,000 personal loan from Mr Robinson.
One in three people now believes Labour is "getting sleazy", while half the public thinks the Government is "getting too arrogant and out of touch". A majority still think Labour "can be trusted", although the figure has dropped since last July.
Mr Blair, who begins a three-day visit to South Africa today at the end of his family holiday in the Seychelles, hopes to turn the tide by getting "back to business" and switching the focus to the Government's plans to improve public services.
But the Prime Minister faced further controversy yesterday as friends of Mr Whelan revealed he intends to write a book exposing the deep divisions at the heart of the Government.
Pressure mounted on Mr Whelan to leave his Treasury post immediately rather than wait until he finds another job. He hopes to stay for a few weeks but Downing Street wants him to quit within days.
David Heathcoat-Amory, the Tory Treasury spokesman, said: "Mr Whelan seems to be timing his departure to suit his own job prospects ... He should be dismissed immediately and given no more access to Budget planning."
Whelan book talks, page 2; Anne McElvoy, Review page 3; Ken Livingstone, Review, page 4Reuse content