The Foreign Office declined to comment on reports earlier in the day the team included special forces soldiers who had been detained in Benghazi by opponents of Moammar Gadhafi's regime.
"The team went to Libya to initiate contacts with the opposition. They experienced difficulties, which have now been satisfactorily resolved,"Hague said in a statement.
Hague said that, in consultation with the opposition, Britain intends to send another team to Libya in due course "to strengthen our dialogue."
Earlier, Hague echoed Defense Minister Liam Fox in telling the BBC that it would be inappropriate to comment on an article in Britain's Sunday Times newspaper that soldiers were captured by rebel forces when a secret mission to put British diplomats in touch with leading opponents of Libya's embattled leader went awry.
When pressed on whether the UK diplomatic team was in danger, Fox had said the government was in contact with the diplomatic team.
"It is a very difficult situation to be able to understand in detail," he said. "There are a number of different opposition groups to Col. Gaddafi in Libya who do seem relatively disparate." The Sunday Times reported that up to eight special forces soldiers, armed but in plain clothes, were captured while escorting a junior British diplomat through rebel-held territory in eastern Libya.
The special forces intervention angered Libyan opposition figures who ordered the soldiers to be locked up on a military base, the newspaper reported.