British pilots have taken part in US and Canadian airstrikes against Islamic State group targets in Syria, despite a vote in parliament in 2013 against military action.

"The UK is not conducting airstrikes in Syria. But we have a long-standing embed program with allies, where small numbers of UK personnel act under the command of host nations," the defence ministry said on Friday.

"That has been the case in Syria, although there are currently no pilots operating in this region," it said, adding that the number of pilots involved was fewer than 10.

In 2013, Prime Minister David Cameron's government suffered a setback when it lost a vote on Syria air strikes because of opposition from the Labour Party.

MPs last year voted in favour of air strikes against IS jihadists in Iraq, but not in Syria.

Eight British RAF Tornados based in Cyprus are carrying out air strikes over Iraq as part of US-led operations and Britain currently also has three spy planes flying missions in the region.

Documents given to London-based human rights group Reprieve, under freedom of information requests, showed that British personnel embedded with US and other coalition forces have operated in Syrian airspace and "include pilots flying strike missions", Reprieve said.

"Documents obtained by Reprieve indicate that UK personnel have already been involved in bombing missions over Syria for some time - making the current debate over whether Britain should carry out such strikes somewhat obsolete," said Jennifer Gibson, a staff attorney for Reprieve.

"It is alarming that parliament and the public have been kept in the dark about this for so long," Gibson said.

Days after 30 Britons were among 38 tourists killed by a jihadist on a beach in the Tunisian resort of Sousse last month, Defence Secretary Michael Fallon hinted that Britain's parliament could be asked to vote again on joining air strikes on targets in Syria.

He told the BBC that IS "has to be defeated in both Syria and Iraq" and that there was "an illogicality" about not being able to strike targets in Syria.

Cameron favours exploring a second vote to gain support for air strikes in Syria later this year after Labour has elected a new leader in September who could give him the support he would need to get the move through parliament.