Speculation about their future at the company has been growing ever since the poor performance of non-executives at last year's controversial annual meeting.
Their decision not to seek re-appointment at the next shareholders' meeting follows the announcement earlier this year that Cedric Brown was stepping down as chief executive.
The row over Mr Brown's "fat cat" pay rise and tension caused by plans to demerge British Gas has cast a cloud over the company for months.
Lord Walker, who as energy secretary was responsible for privatising British Gas, was regarded as part of the company's old guard and rumoured to be an opponent of the break-up plan. He had been at the company since 1990.
Relations between the executive directors and Mr Boissier, chairman of Pressac, and another non-executive, Dixons chairman Sir Stanley Kalms, were also thought to be strained. Mr Boissier has been at British Gas since 1981.
Lord Walker said he was going because a further three-year contract would have taken him beyond normal retirement age. However, he will continue to advise the company on its activities in the Far East and Latin America. Mr Boissier said he had been planning to step down for some time.
Despite receiving flak over service contracts from outraged shareholders at the last annual meeting, British Gas has decided not to follow the Greenbury Committee's proposals.
The company's annual report, out yesterday, said it would not be reducing service contracts from two years to one because it "believes that flexibility is required, especially when recruiting from outside".
The report also reveals that two former executive directors who resigned last year received combined pay-offs of pounds 544,000, although this was less than the maximum they may have been entitled to receive.
Russell Herbert received pounds 241,775, representing 15 months' pay, despite having a two-year rolling contract. Howard Dalton, also on two years, received one year's money of pounds 303,420. A spokeswoman said the pay-offs were reached by mutual agreement.
The annual report reveals that only Roy Gardner, recruited in 1994 to become finance director, received a pay rise. His salary rose pounds 15,000 to pounds 300,000.Reuse content