Operation Panther's Claw, which claimed their lives in ferocious fighting, was meant to improve security in the Babaji district of Helmand.
But only 150 of the 80,000 potential voters there braved Taliban threats to vote last week, it was reported yesterday.
The astonishingly low turnout in the presidential election poses massive questions about the war against the Taliban and the wider British role in Afghanistan.
Last night the grieving mother of one of the soldiers expressed anger and despair that each British death was worth only 15 Afghan votes.
Hazel Hunt, whose 21-year- old son Richard was killed by a Taliban bomb, said: 'It makes you go numb when you hear something like this. It horrifies me. The figures reflect terribly on our strategy in Afghanistan.'
The voting report is a further blow to Defence Secretary Bob Ainsworth, who had specifically linked Panther's Claw to making the area safe.
On the day of the election, he said: 'Operation Panther's Claw was a tough fight, but it has brought nearly 80,000 Afghans out from under the tyranny of the Taliban and ensured that they can take part in this election.'
Panther's Claw was launched in June to clear the Taliban from rural areas.
As well as the ten British troops killed in the operation itself, at least 14 more died as the Taliban responded by stepping up attacks in other areas.
Altogether, 207 British troops have died since the U.S.-led invasion of Afghanistan in 2001.
The apparent spectacular failure forced the UK ambassador to Afghanistan to defend our military effort yesterday.
More...British soldier dies in hospital a week after he was wounded in Afghanistan explosion
MAIL COMMENT: Ten soldiers give their life to let only 150 Afghans vote - is this mission impossible?
Mark Sedwill did not deny the figure of 150 voters, reported by the BBC, although he said it was too early to tell the exact turnout.
But he admitted many people were intimidated by Taliban threats to cut off fingers marked with the indelible ink which showed someone had voted.
Mr Sedwill also claimed the offensive had never been aimed specifically at providing security for last week's elections.
He said: 'This operation was going to happen at some stage anyway.'
His summary of the aim of Panther's Claw directly contradicts both Gordon Brown and Foreign Secretary David Miliband.
Mr Miliband said last month the operation 'will bring a further 80,000 people back under the authority of elected government. These people should also be able to participate in the elections.'
Mr Brown, speaking on the day of the poll, said: 'I want to thank our British forces for everything they have done to make sure these elections can take place.'
Last night Liberal Democrat spokesman Nick Harvey said: 'If the turnout is as spectacularly low as suggested, then clearly one of the objectives has not been met.
'The Government was too ambitious in claiming what could be achieved in this election. It is regrettable, but no huge surprise, that in areas where the fighting has been most intense, the turnout has been lowest.'
Military insiders questioned the wisdom of launching Panther's Claw a few weeks ahead of the elections, with little time for 'liberated' people to gain confidence in their security.
One senior former Army commander told the Daily Mail: 'I'm sorry to say it makes you wonder if this operation was really worthwhile.
'It cost a lot of British lives, but one has to ask, if we wanted Afghans to come out and vote was unleashing a major battle on their doorstep just a few days before polling day really the best way?'
Air Vice Marshal Andy Pulford, assistant chief of the defence staff (operations), said: 'British forces know exactly what they have fought for. They know with their own eyes the improved quality of life now enjoyed by thousands of Afghans in Babaji.
'Low voter turnout or not - and this has yet to be verified - that security will be enduring.'
The Foreign Office said it was 'wrong' to speculate on turnout before the votes were counted.
A spokesman said: 'At the moment reports and paint an incomplete picture. We always knew these elections were going to be held in extremely challenging circumstances.'
Latest results yesterday showed President Hamid Karzai extending his lead over former foreign minister Abdullah Abdullah.
With votes from 17 per cent of polling stations counted he had 44.8 per cent with Mr Abdullah on 35.1 per cent.