Britain then also became part of the Nato-led Isaf mission to stabilise the country and support its new government after the Taliban were toppled from power.
Back in 2001, there was a widely held sense of "mission accomplished" as it appeared the Taliban had been routed and - even if Osama Bin Laden had not been captured - al-Qaeda put on the run.
In the following years, the world's attention shifted to events in Iraq and the US-led invasion in 2003.
With British and US forces fighting hard in Iraq, Afghanistan became the forgotten campaign.
It was only when British forces were sent into Helmand province - a Taliban stronghold - in 2006 that operations in Afghanistan once again made the headlines as the death rate rose unexpectedly rapidly.
Caroline Wyatt analyses the British casualty toll in Afghanistan
The hope, expressed by then Defence Secretary John Reid, that British forces might leave without a shot being fired was a forlorn one, and now sounds hopelessly naive as British troops see some of their fiercest fighting in years.
Repatriations of fallen soldiers to the UK are becoming commonplace
So far, they have fired more than four million bullets, in a campaign which has cost £5.6bn and 184 British lives - 15 of them this month.
Commanders say the recent rise in the death toll among British and several other coalition forces - most notably the US, which provides the bulk of troops in Afghanistan - is largely down to the current offensives against the Taliban.
That new focus has come from the top in Washington, with the election of President Barack Obama, the publication of a new Afghanistan/Pakistan strategy and the appointment of a new Isaf commander.
The strategy of General Stanley McChrystal is first of all a military push against the Taliban to extend security, in the kind of operations now being seen in Helmand.
The new Isaf commander has made it clear "the population is the prize", and the military effort must go hand-in-hand with progress on the civil side.
Gen McChrystal has warned against causing civilian casualties, which have alienated many Afghans.
Greater security is essential to the rebuilding effort and to give time and space for good governance to emerge.
And good governance - if it does grow - would help security by convincing the Afghan people that foreign troops are supporting an Afghan state that can bring tangible benefits to their lives.
We can't cut and run from this one. We can't afford to lose
Military historian Allan Mallinson
The relative lack of progress on so many fronts, though, over the past years under President Hamid Karzai has been one of the main Western frustrations.
The levels of corruption within the Afghan government, its ineffectual reach in many provinces and the lack of a real justice system, or yet an effective police force, have all made it harder to convince the Afghan people that they are much better off now.
Despite this, only 23% of people in southern Afghanistan are said to support the Taliban, while support for the Isaf coalition has remained reasonably high despite the campaign's problems.
There is now a gritty realism dawning in the campaign, and the public acknowledgement of just how difficult all this will be in the world's fourth-poorest country, which has been torn and scarred by war for the past three decades.
Many of the Afghan middle classes who might form the backbone of the new Afghanistan have long since fled abroad, though some remain.
The current focus on Helmand by 9,000 British and now an extra 10,000 US troops is because the province remains one of the Taliban's strongholds and the producer of more than half of the country's opium crop.
The US and UK appear to have dropped the original policy of trying to eradicate the poppy crop before providing alternative livelihoods for Helmand farmers, a policy which had alienated potential allies.
The US and British forces want to stabilise Helmand in time for next month's Afghan presidential elections.
UK forces are engaged in a major offensive in Helmand
And although the operation is proving costly in terms of casualties, it is seen by many as a defining moment in this long and tough campaign.
Without visible progress this year, the momentum - and the overall campaign, not just in military terms - could be lost.
Military historian and former cavalry commander Allan Mallinson says Britain simply cannot afford to fail in Afghanistan, especially after Iraq.
"With Afghanistan, we're clearly in it for the long haul if we are to see any results," he says. "We can't cut and run from this one. We can't afford to lose."
But he and others have expressed fears the government has still not committed all the resources the UK contribution to the Isaf campaign needs, from more helicopters to higher troop numbers.
Many have warned that a long and difficult road lies ahead in Helmand province and that there will be more casualties this summer and beyond.
For some, though, the question marks remain over how long Britain and Nato's resolve will last - and whether the Taliban's will last longer.
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