The Russian Foundation, a group part-funded by democrats in the country, has called on APCO, LLM Communications and Luther Pendragon to argue its case.
It is urging the Government to recognise that Russia under Putin has clamped down on media freedom and appears to be closing pluralist institutions and moving towards a reconcentration of power.
'The Russian Foundation has been set up to create a more informed platform for discussion about Russian-related issues,' said APCO Europe chairman Brad Staples. 'It is aimed at opinion leaders to ensure they get access to academic reports, policy events and media.'
The group so far has the public support of former foreign secretary Robin Cook, who contributed to a recent pamphlet by think-tank The Foreign Policy Institute warning of developments under Putin.
On the other side, Ria Novosti - the Russian equivalent of the British Council - has for a couple of years employed its own triumvirate of advisers in Britain. Brown Lloyd James, Media Strategy and Portland PR have been running an ongoing 'hearts and minds' campaign targeted at business, political and cultural audiences.
It includes putting the case that Russia is not straying from its economic and democratic reforms.
Tensions between Putin and the West surfaced on the global stage last autumn over his support for the ultimately defeated Ukrainian president Victor Yanukovich.