Liberata head of strategy Charlie Bruin said: 'We want to have regular soundbites [in the media] and consistent press coverage around our target markets.'
Cubitt will highlight the advantages of outsourcing following the 2004 Gershon Review, which outlined requirements to achieve greater public sector efficiency.
The brief also includes lobbying against VAT on outsourcing and liaising with MPs around regeneration and job creation in the North-West of England.
Liberata has 22 local authorities on its books and works for financial services firms such as JPMorgan and Barclays Life Assurance.
Cubitt partner Ross Gow leads the account, supported by associate director Desiree Maghoo. They report to Bruin and Liberata CEO Robert Gogel, who joined from tech software firm RebusIS last September.
Liberata said it picked Cubitt because of the agency's 'prior relationship' with Gogel, which it declined to detail.
In 2005, Liberata became the first outsourcer to be regulated by the Financial Services Authority. The firm turns over £220m a year, and employs 4,000 staff.