The incumbent, which had held the business for 12 years, will join a shortlist of up to four agencies in the pitch to retain the multimillion-pound account.
British Gas is keen to promote itself above and beyond an energy supplier, and wants the winning agency to come up with a strategy that will help it retain more customers.
The pitch is being handled by the Haystack Group, which is currently whittling down a list of six agencies to a final pitchlist. The company is expected to announce the winning agency by April.
The director of marketing and strategy for British Gas, Nick Smith, said: "Our emerging strategy for the British Gas brand as a provider of services to the home means this is an exciting time for marketers to be working with us. We have had a long and successful relationship with BMP, and I know it is keen to continue with that good work."
He added that the changing position of the company needed to be communicated to consumers in order to retain them in a less competitive marketplace.
British Gas products include telecoms, heating and plumbing and security services. Its parent company Centrica owns the AA, the financial company Goldfish and the telecoms company One.Tel as well as British Gas.
The Haystack Group managing director, Suki Thompson, said: "We are looking for an agency that can take the current strategy on to the next stage, as well as providing the service levels required for this major account."
The pitch follows British Gas' decision last year to centralise its media planning and buying into Carat after a pitch involving the incumbent, Carat, OMD UK, MindShare and Zenith Media.