The group, which has 22 million customers and assets of more than £400bn, is keen to raise awareness among MPs, MSPs and Welsh Assembly members of its value products, such as high-interest accounts.
It will also publicise research, such as the Halifax House Price Index, and the work of its community investment programme, the HBOS Foundation.
HBOS government relations executive Laura Chisholm said 'social banking' was also an important area following December's pre-Budget target to halve the number of 'unbanked' households within two years.
HBOS has two thirds of the UK market for basic bank accounts.
Chisholm added: 'We operate in a public policy environment, so it is important we have a dialogue with people from that environment. MPs have relationships with their constituents, who are in turn our customers, so MPs are important stakeholders.'
HBOS, whose major brands include Bank of Scotland, awarded the account to F-H in a three-way pitch against Consolidated Communications and Four Communications.
The account will be led by F-H director Julie Harris, who reports to Chisholm and HBOS general manager of group communications Shane O'Riordain.