APCO Worldwide's UK-based public affairs team will work to engage the British Government to continue its support for the drive.
Britain has contributed £166m since 2008, most recently distributing £40m in 2012, but has not made any pledges relating to funding from this year onward.
Rotary International, which is the umbrella association for the philanthropic Rotary Club movement, has also appointed APCO to the same brief in Germany, France, Brussels and Canada.
Nigeria, Pakistan and Afghanistan are the only countries where the disease, which Rotary started fighting in 1979, is still endemic.
Rotary is part of the Global Polio Eradication Initiative, a public-private partnership set up in 1988 to implement the World Health Assembly's call for the eradication of polio. It is led by national governments but spearheaded by the World Health Organization, Unicef, Rotary International and the US' Centers for Disease Control.
James Acheson-Gray, MD of APCO Worldwide in the UK, said: 'We look forward to helping Rotary International's advocacy efforts to push this issue further up government agendas in Europe and to fully activate and leverage Rotary's network of 1.2 million members worldwide.'