The yacht, owned by Sail Bahrain, was seized on November 25, a day before it was due to take part in the Dubai-Muscat Offshore Sailing Race.
The foreign ministry in London said all the sailors were understood to be safe and well and their families have been informed.
The Dubai-Muscat 360-nautical mile (667km) race, which first took place in 1992, passes through the Gulf into the Indian Ocean, via the Strait of Hormuz, before arriving in Muscat, the capital of Oman.
David Miliband, the UK's foreign minister, said: "FCO [foreign ministry] officials immediately contacted the Iranian authorities in London and in Tehran on the evening of 25 November, both to seek clarification and to try and resolve the matter swiftly.
"Our ambassador in Tehran has raised the issue with the Iranian foreign ministry and we have discussed the matter with the Iranian embassy in London.
"I hope this issue will soon be resolved. We will remain in close touch with the Iranian authorities, as well as the families."
In March 2007 a group of 15 British sailors were seized by Iran while sailing in disputed waters.
They were released after about two weeks, but only after a tense diplomatic standoff between Iran and the UK.
Relations between Tehran and the West have deteriorated after the Islamic Republic announced on Sunday that it plans to build another 10 uranium enrichment plants.