This will be the first time esure has hired an agency to handle its public affairs.
Last month, esure became the first UK insurer to announce that it would not offer home insurance cover to residents living within postcodes in the UK that it identified as being prone to - or at risk of - flooding.
Esure's decision was raised in Prime Minister's Questions and became the subject of an Early Day Motion.
In Scotland, local authorities, the Scottish Executive and local flooding appraisal groups have already taken steps to mitigate flooding by making flood defence a statutory duty.
Esure believes the rest of the UK should follow suit and has tasked Consolidated with assisting in communicating this message to key audiences.
Consolidated PA Director Ed Vaizey said: 'In Scotland they have a clear line of communication between Government and local authorities on this issue which we'd like to see brought into effect in the UK.
'We'll be briefing esure before its appointments with MPs and advising it on any parliamentary activity or policies that will affect it directly.'
Director Ilan Jacobs will run the account, reporting to Adrian Webb, the former Consolidated consultant who now heads PR for esure.
Jacobs joined Consolidated in 1999 and formerly worked for ex-cabinet minister Peter Mandelson and Downing Street opinion polling guru Philip Gould.