British newspapers say Prime Minister David Cameron this week will announce the withdrawal of at least 500 troops from Afghanistan by the end of 2012.
The move, expected to be announced Wednesday, follows last month's announcement by U.S. President Barack Obama that 10,000 American troops will be withdrawn this year as part of a process of handing security over to Afghan forces.
Further withdrawals planned for 2012 are to reduce U.S. troop numbers in Afghanistan to about 68,000.
Prominent U.S. Senator John McCain on Sunday criticized Mr. Obama's drawdown plan as an "unnecessary risk" that was not supported by U.S. military commanders.
McCain, the Republican Party's presidential candidate in 2008, made his comments to CNN from Kabul.
Britain has the second-biggest foreign contingent in Afghanistan -- some 9,500 troops -- with the majority in southern Helmand province, one of the most violent areas.
Also Sunday, the chief of staff of Germany's armed forces said Germany would reduce its troop levels in Afghanistan by about 500 at the end of the year.
Germany has about 5,000 troops in northern Afghanistan.