The seven men were placed on the United Nations list because they were suspected of having links with al-Qaeda and the Taliban.
As a result they have been barred from leaving Britain and their assets have been frozen by the Bank of England and HM Treasury.
They include individuals who were:
* convicted of involvement in the 2003 Casablanca bombings and of possessing terrorist documents in the UK,
* accused of assisting the 1998 bombings of two US embassies in Africa and of being an associate of Osama bin Laden,
* found guilty by a military court of plotting terror attacks.
But an attempt by the men to have their names removed from the UN list has now won the backing of the Foreign and Commonwealth Office (FCO).
The FCO has insisted that it is acting because it has reviewed the men's cases and does not think they are dangerous.
However, sources in Washington said the move by the British Government risked worsening relations between the US and UK at a time of heightened concern over security. The men are also named as suspected Islamist extremists on a US Treasury list barring them from travel to the United States.
The Obama administration is determined to tighten up the country's border controls in the wake of the failed attempt to blow up a transatlantic jet on its approach to Detroit airport by Umar Farouk Abdulmutallab, a Nigerian who spent three years in Britain studying at University College London.
Washington is unlikely to relish the prospect of removing a number of men classed as terror suspects by the UN from its own watch lists, or of having to unblock any financial assets the men may have in the States, as a result of diplomatic pressure by Britain .