The style has already been set, with the President's decision to add a London leg to next week's trip to Europe for the Nato/Russia summit - and thus send a signal of Washington's desire to turn the page after its difficulties with the previous Tory government under John Major.
Though relations improved later, they were soured by the help the Conservatives gave George Bush during the 1992 campaign, London's fury over the US visa granted to the Sinn Fein leader, Gerry Adams, in 1994, and widespread resentment in Washington at what was seen as Britain's refusal to get tough with the Bosnian Serbs.
Not only is the Blair government free of all such baggage, it has also given itself added credibility by a more constructive approach to Europe. As Mr Cook himself put it last week: "Britain will be of more value as an ally to the US if it emerges as a strong force in Europe."
All these factors will be working to Mr Cook's advantage in his visit, shoehorned into an exceptionally tight schedule for an incoming Foreign Secretary. Having arrived in America last night, he leaves this evening for Amsterdam and a special session of EU foreign ministers to prepare Friday's informal Inter-governmental Conference summit in Holland.
Top of the agenda today will be Nato enlargement, and the forthcoming handover in Hong Kong. Britain's immediate aim is to ensure the US keeps a close eye on China's behaviour once it has taken power in the former colony - not a difficult task given the Sinophobic mood in Washington. In keeping with the new "ethical dimension" of foreign policy, Mr Cook may also sound out the Administration on sanctions against countries like Indonesia and Nigeria with dubious human rights records.
Mr Cook will hold separate talks with his opposite number, Madeleine Albright, the Defense Secetrary William Cohen, Sandy Berger, the President's national security adviser, and Jesse Helms, chairman of the Senate Foreign Relations Committee. A session with Mr Clinton himself would be an unlikely, and unexpected, bonus.Reuse content