Public opinion is almost evenly divided over the UK mission in Afghanistan but support has grown since 2006, a poll for the BBC and the Guardian suggests.
Criticism of the UK's Afghan strategy is mounting, with 15 soldiers killed in the first 10 days of the month.
But the poll of 1,000 adults, conducted as news of the casualties emerged, found 46% backed the British operation in Afghanistan while 47% opposed it.
A similar poll in 2006 found 31% backed the UK's action while 53% opposed it.
Figures in the poll carried out by ICM Research over Friday and Saturday for BBC Newsnight and the Guardian newspaper found support for the conflict among men had risen from 40% to 49% while for women, the figure has gone from 22% to 43%.
However, it also found that 42% of people wanted troops to pull out of Afghanistan now while 36% backed them to stay as long as needed.
UK troops have spent recent weeks on an offensive - codenamed Panther's Claw - which is designed to increase security ahead of Afghan elections planned for next month.
But the surge has brought a big increase in casualties, with 15 servicemen killed in the first 10 days of the month.
It means 184 service personnel have now died in Afghanistan since 2001, more than the 179 who were killed during the war in Iraq.
British troops in Afghanistan are due to hold a private memorial service at Camp Bastion to remember the eight men who died last week in a single 24-hour period.
Prime Minister Gordon Brown said the mission was showing signs of success and reiterated his praise for UK troops.
"Our troops are making progress as they attempt to make the area safer. Despite the losses, our forces are doing a magnificent job in moving forward," he said.
Defence Secretary Bob Ainsworth said there had been a massive improvement in personal kit and equipment, as well as vehicles, for troops in Afghanistan.
But critics have claimed that more troops needed to be sent to the region and there have also been calls for more helicopters.
Newsnight will reveal more details of the survey on BBC Two at 2230 BST on Monday 13 July, and the programme will subsequently be available on BBC iPlayer.