Mr Cook, who leaves today for his first visit to Washington as Foreign Secretary, will raise the Hong Kong issue with the US Secretary of State, Madeleine Albright.
In what will be seen as a coup for Mr Cook, Ms Albright has agreed to be present at the hand-over ceremony in Hong Kong on 30 June, underlining the US administration's interest in the future of the British colony after June. The Foreign Office is keen to internationalise its concerns over human rights in Hong Kong, aware that it will have a limited amount of influence over developments there once Britain withdraws. Britain wants US and other international support for its efforts to monitor conditions there when it leaves.
Tony Blair, the Prime Minister, will discuss the concerns about the hand- over with Chris Patten when the governor of Hong Kong visits London this week.
Mr Cook's visit to Washington is seen as a goodwill gesture, ahead of a full-scale meeting between President Clinton and Mr Blair.
Relations between the administration and the new British government are said to be warm, with Mr Blair and President Clinton enjoying a good rapport. Mr Cook, who may also meet the vice-president Al Gore, is also expected to raise other big international issues, including the expansion of Nato and the situation in Bosnia, where the US believes that the Dayton accord could be better implemented.
A common front on Bosnia is more complicated because the US administration has promised Congress that the international force there will leave by the middle of next year. The Foreign Office is thought to favour a longer- term presence if necessary.