LONDON — Already struggling with an economy on the brink of recession and a record budget deficit, Britain is facing a potential new problem: an exodus of British companies fleeing the tax system.

In the last week alone, three companies have announced plans to move their headquarters abroad before the end of the year. They say they are trying to cut their tax bills and frustrated by a lack of clarity about future tax rules.

The Henderson Group, a London-based asset management firm, and Charter, an engineering company, plan to move to Ireland. The Regus Group, the office space and business services provider, is leaving for Luxembourg. And at least two more companies, the advertising agency WPP Group and insurer Brit Insurance, said they might follow.

The moves, which have started intense discussions among lawmakers and businesses about the competitiveness of Britain’s tax system, could not come at a worse time. The government is expected to take in billions less in tax revenue because of losses at financial firms affected by the credit crisis. Merrill Lynch, for instance, may avoid paying taxes here for years after booking $29 billion in losses related to the United States subprime mortgage market through its British unit.