Support forces are in addition to the 21,000 troops announced by Obama, US daily says.
A sharp rise in military casualties has fuelled public dissatisfaction over the UK’s involvement in a conflict that has now cost more British troop lives than the invasion and occupation of Iraq.
The past year has been the most deadly for British forces in Afghanistan, with more than 50 fatalities since June, taking the total in the eight-year conflict to 221.
Critics, including some senior military commanders, have accused the government of failing to provide troops with enough of the correct equipment.
British politicians said on Tuesday that military vehicles and helicopters in Afghanistan were suffering from a shortage of spare parts, with equipment in Britain being cannibalised to fill gaps.
Simon Lewis, Brown’s spokesman, said: “Any decisions on troop numbers … would be subject to a number of conditions, including that they should be properly equipped and that we are in agreement with our other allies about what we need to do on the ground.”
The opposition Conservative Party, leading in opinion polls ahead of an election due by the summer of next year, have said troop numbers should only be increased to help train the Afghan army and bring forward the day that British soldiers could return home.
Lewis said if there was an increase in troops it was possible they would be involved in training, but not exclusively.
A survey on Wednesday shows more than a third of UK voters believe all British forces should be withdrawn.
|A sharp rise in UK casualties has fuelled public disquiet over involvement in the war [EPA]|
The figure has increased to 36 per cent from 29 per cent in mid-September, the Populus poll for The Times newspaper showed.
Women are driving the growing unease at Britain’s deployment, with four out of 10 wanting British forces out, up from three out of 10 over the past month.
There are now more than 100,000 foreign troops in Afghanistan, most of them from the US.
The US has 65,000 troops there and is expected to raise that figure to 68,000 later this year.
Barack Obama, the US president, is considering a recommendation to boost his force with a further 40,000 troops next year.
Hamid Karzai, the Afghan president, said on Tuesday he would welcome more US troops, but said the number should be determined by military experts.