The Russians responded immediately because the aircraft had strayed over the most sensitive military zone in the country, the Baltic enclave of Kaliningrad on the Polish border.
The Foreign Office said it could not confirm the details, because it has not been able to speak to the two Britons, Cliff Davidson and Mark Jeffrey, who are both thought to be in their 40s.
They were expected to leave Russia for Poland either last night or this morning.
"We were trying to land in Gdansk [in Poland] but the wind was too strong," one told ITN.
Russian authorities announced earlier that they would not be charged for encroaching on the airspace of the highly militarised Kaliningrad enclave, home of Russia's Baltic fleet.
The Russians sent a Su-27 fighter jet to bring the plane down after it was blown off-course by high winds while flying over the Baltic on Thursday.
According to the Foreign Office the two Britons sent out a mayday distress signal and were guided by the military plane to Khrabrovo airport in Kaliningrad, which is cut off from the rest of Russia and bordered by Lithuania and Poland.
They were questioned by border guards and customs officers, but it was decided they had committed no crime.
A Foreign Office spokesman said he could not confirm what kind of plane they were in.
"We have seen the reports. We are pleased they are safe.
"They have not contacted us and until we speak to them, we cannot clarify the matter."Reuse content