1,000 British soldiers were amongst Operation Moshtarak's 15,000 ranks
Sixty-four per cent of British people think the war in Afghanistan is unwinnable, a BBC poll suggests.
More than two-thirds (69%) also think the government has not done all it can to support British forces fighting in the country.
Only 27% agree that the government has given sufficient support to UK forces.
The poll was conducted for the BBC's Newsnight programme and included a random sample of 1,004 people in England, Scotland and Wales.
The data was collected between 19-21 February 2010, while more than 1,000 British troops were taking part in Operation Moshtarak as part of a 15,000-strong Nato and Afghan offensive against the Taliban in Afghanistan's Helmand province.
Newsnight commissioned the poll, conducted by ComRes, to assess what people think about Britain's involvement in the ongoing conflict in Afghanistan.
The war began in 2001 in response to attacks against the US on 11 September. Since then, 263 UK military personnel have been killed.
Speaking at a 70-nation London summit on the future of Afghanistan in January, the prime minister said that mid-2011 should be the deadline for "turning the tide" in the fight against insurgents in Afghanistan.
But 63% of respondents to the Newsnight poll agreed when asked if they thought that whoever formed the next government after this year's general election should commit to removing Britain's armed forces from Afghanistan by the end of 2010.
It is widely expected that a general election will take place in early May.
When asked whether the war in Afghanistan was unwinnable, older people were gloomier than the young about the prospects of success. Seventy per cent of people aged 55 and over agreed that the war was unwinnable, compared with 58% of those aged 18-24.
Otherwise, the response to this question was virtually unchanged since polling last November, suggesting that Operation Moshtarak might not have made an impact on the public.
Watch Newsnight's special programme on defence on Tuesday 23 February 2010 at 2230 on BBC Two.