Panther's Claw saw the biggest monthly death toll since 2001
The UK ambassador in Kabul has defended the use of soldiers to protect Afghan elections - despite low voter turnout.
Mark Sedwill was responding to reports that just 150 people voted in an area where 10 UK troops died fighting the Taliban ahead of the elections.
He insisted the offensive was not just about the elections, and total turnout in Helmand province was not yet known.
Ministers also said it was too early to tell voter turnout and that speculation over figures had been "contradictory".
However Mr Sedwill admitted turnout had been lower than expected in some areas and there had also been irregularities.
When the offensive began, the Ministry of Defence had said the primary aim of Operation Panther's Claw had been to pave the way for safe elections in areas dominated by the Taliban.
There is some evidence, but it is still anecdotal, that people from outlying areas travelled into the more secure areas like Lashkar Gah
The BBC's Caroline Hawley said the focus of the military operation had been Babaji district in Helmand province, where 10 UK soldiers have been killed.
Our correspondent added that reports that about 150 people voted there, out of an eligible population of 55,000, had not been disputed by officials in Afghanistan.
Launched in June, 22 servicemen have died during Panther's Claw, and July saw the biggest monthly loss of British soldiers since operations began in Afghanistan in 2001.
Mr Sedwill told the BBC there was some doubt over the figure of 150 voters.
He said: "There is some evidence, but it is still anecdotal, that people from outlying areas travelled into the more secure areas like Lashkar Gah in order to vote in these areas because they felt more confident in doing so.
"So what we don't yet know is the extent to which people moved around and whether turnout was differential, if you like, across that area."
However Mr Sedwill admitted that turnout had been lower than expected and that there had been electoral irregularities across the country.
But he also said he was fairly satisfied with the overall credibility of the election.
Mr Sedwill added: "The test of success for these elections is whether the outcome reflects the will of the people and therefore the winner has a genuinely national mandate.
"That's the test we have always set, rather than focusing on individual elements of the process or the inevitable irregularities that we know would happen across the country."
A Foreign Office spokesman said: "It is wrong to speculate on turn-out before they have finished counting and verifying the ballots. At the moment reports are anecdotal and paint an incomplete picture."
A Ministry of Defence spokesman insisted British troops "know exactly" what they are fighting for and that their efforts had brought security to the region.
The spokesman added: "Low voter turn out or not - and this has yet to be verified - that security will be enduring."