Britain's role in meddling in Iranian politics in the past is well documented, such as its part in overthrowing the elected government in 1953 alongside the USA. At the same time no brutal, corrupt and hated regime anywhere in the world will ever admit to the existence of any discontent that has not been stirred up by outside forces. We cannot rely on what the politicians from either Britain or Iran tell us but must look at whose interests are served by any particular event.
It is clearly in Khamenei's and Ahmadinejad's interests to use longstanding and widespread distrust of Britain's imperialist history to portray the protests as serving outside interests and so try to undermine their legitimacy and popularity. The expulsion of two diplomats, the refusal to renew a BBC reporter's visa and the arrest of Embassy staff can all help in this.
Of course, the Islamic regime came to power after the fall of the Shah whose reign had been assured by previous regime change engineered by the USA and Britain, and these powers obviously want to undermine it. Their adventures in Iraq and Afghanistan have taken out or weakened some of Iran's most important rivals, Saddam Hussein and the Taliban, increasing its weight as a regional power to rival Israel with or without nuclear weapons, and this is clearly a problem for US strategy. They have to do something about Iran.
The sabre-rattling of the Bush administration, which defined Iran as part of the ‘Axis of Evil', has been replaced by Obama's strategy of dialogue and diplomacy: "In offering negotiation and conciliation, [President Obama] has put the region's extremists on the defensive" as Senator John Kerry explained (BBC news online). In order to pursue this strategy the USA has certainly joined in all the hypocritical international condemnation of the repression, but has done so in Obama's measured tones "We call on the Iranian government to stop all violent and unjust actions against its own people". Britain has also remained measured in criticism despite needing to protest against the arrest and possible trial of Embassy staff. The BBC Persian service and Voice of America are undoubtedly giving voice to more protest than the Iranian regime can tolerate, particularly now with its divisions uncovered, and in the long term this is intended to undermine it; but in the short term they have nothing to gain from the present protests getting out of hand.