Around 3,000 forces personnel have taken part in Operation Panther's Claw
The commander of forces in Afghanistan has hailed the latest UK operation a success, as its first stage ended.
Brig Tim Radford was "cautiously optimistic" about the future but said there was "a long way to go" to improve security in time for elections.
Since June, Operation Panther's Claw's first phase involved 3,000 personnel. Ten died. Troops are now trying to hold areas won from the Taliban.
Two more soldiers died in separate blasts on Monday, defence chiefs said.
One of them - a soldier from the Light Dragoons - had been on vehicle patrol in Lashkar Gar as part the second phase of Operation Panther's Claw, aimed at holding the ground.
The other, from 5th Regiment Royal Artillery, was killed while on an unrelated foot patrol in Sangin district.
Earlier, Bombardier Craig Hopson, 24, from Castleford, west Yorkshire, was named after he was killed in an explosion on Saturday. He was serving with 40th Regiment Royal Artillery.
The Panther's Claw offensive ended as UK Foreign Secretary David Miliband urged Afghanistan's leaders to build a political coalition which included some of the country's more moderate insurgents.
Paul Reynolds, BBC world affairs correspondent
The military view of the Miliband proposal to talk to moderate Taliban is that nobody in the Taliban will talk unless it is significantly beaten on the ground.
The military priority right now is to clear ground, hold it and develop its civilian and governmental structures.
This is why Operation Panther's Claw, to clear the Taliban from populated areas in north central Helmand (and a similar offensive conducted by US marines in the south), is seen as so important.
Lt Gen Simon Mayall, British deputy chief of operations, said: "The Taliban is really worried about our policy of clear and hold.
"It gives us the chance to get 'second-tier' Taliban to re-engage with the government and this is at the heart of our policy."
So the success of the "Talk to the Taliban" approach much depends on there being military progress.
But, equally, military success will not last unless political progress is made.
British Prime Minister Gordon Brown said it had been "one of the most difficult summers" since UK forces entered Afghanistan in 2001.
He said the offensive had secured land for around 100,000 people and had started to break the "chain of terror" linking Afghanistan and parts of Pakistan to the UK.
"It's time to commemorate all those soldiers who have given their lives and to thank all our British forces for the determination and professionalism and courage that they've shown," he added.
Operation Panther's Claw focused on an area the size of the Isle of Wight, between Helmand's provincial capital, Lashkar Gah, and its economic capital, Gereshk.
The Ministry of Defence said the first stage was the most heavily-militarised of the offensive.
During the month-long push, troops came across 153 improvised explosive devices, or roadside bombs.
It ended with a final armoured thrust into former Taliban territory by The Black Watch and 2nd Battalion The Royal Welsh.
Ten soldiers died during the offensive, while another 10 were killed on unrelated missions during the last month.
Brig Radford said the casualties had not been in vain.
"I am absolutely certain that the operation has been a success," he said.
"We've had a significant impact on the Taliban in this area - both in terms of their capability and their morale."
British commanders estimate there were up to 500 Taliban in the area before the start of the operation and say most have now fled, given up arms or been killed.
Brig Radford said Afghan nationals had moved back into the cleared areas and had been warning them about roadside bombs and helping them plot safe routes.
These good relations meant some reintegration with current insurgents was "not beyond the realms of possibility", he said.
"We have started to break the chain of terror that links Afghanistan to the streets of Britain"
The operation's second and third stages will aim to hold ground taken by forces during the offensive and work towards the elections in late August.
Brig Radford said morale was "extremely high" among British troops, adding that he did not feel his forces had been short of helicopters during his three months leading them.
The high casualty rate among British troops, with roadside bombs proving particularly deadly, had provoked debate over whether forces were properly equipped to deal with the threat.
Much of it had focused on a perceived lack of helicopters, with Conservative leader David Cameron attacking ministers over the "scandal" of shortages.
Military commanders said using more helicopters would save lives by keeping troops off the roads and making their movements less predictable.
However, Mr Brown has insisted troops had the resources "to do the job" and that lives had not been lost during the operation because of a lack of helicopters.