The Prime Minister has also asked ministers to meet their German opposite numbers, if possible before Christmas, in a drive to create a new Anglo- German alliance.
The Downing Street memo will infuriate Eurosceptics who already claim that the Government is "selling out" to Brussels.
Mr Blair hopes greater co-operation will ensure that Britain is not sidelined when the single currency starts. He is concerned that the UK, which will not join the euro in the first wave, will be left behind as other countries become closer.
Mr Blair believes that the Schroder administration in Bonn is crucial to the centre-left majority which has won power across Europe. In his letter, described by one source as a "rallying cry", Mr Blair instructed the Cabinet to pay more attention to Europe.
He urged ministers to deepen their relationships with their counterparts in other EU states and to make sure that their officials exchanged information with their opposite numbers. It was essential ministers proved their European commitment since Britain's EU presidency had ended, the memo said.
A number of joint working parties has already been set up. However, there are growing signs of frustration with Britain in Bonn, over tax harmonisation, and Paris, over Britain's attempt to muscle in on the Franco- German axis, despite Downing Street's attempts to portray Mr Blair as the moderniser giving credibility to more left-wing governments.
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