The soldiers were on patrol in Helmand province at the time of the blast on Tuesday evening (local time).
British Prime Minister David Cameron said the deaths marked a "desperately sad day for our country."
The attack is certain to fuel calls for the acceleration of a planned withdrawal of all US-led coalition troops from Afghanistan by the end of 2014. The war has become increasingly unpopular in the United States and among its NATO partners in Europe.
Washington has also grown frustrated with the administration of President Hamid Karzai, who has been making increasing demands of America in order to sign a deal that will allow some troops to remain past 2014, mainly in a counterterrorism and training role.
Helmand has been the deadliest province by far for coalition troops since the Afghan war started over a decade ago. Most of Britain's 9,500 soldiers are based there, and the province also has thousands of US troops.
The Taliban have fought fiercely for control of Helmand because it accounts for about half of all poppy production in Afghanistan. Poppy is the main ingredient in making opium and has been a significant source of revenue for the militants.
So far this year, 54 NATO troops have been killed in Afghanistan, including 38 from the United States and four from Britain.
Britain has lost more troops in Afghanistan- 404 after Wednesday's killings - than any other country except for the United States, which has counted at least 1780 deaths as a result of the US-led invasion in late 2001, according to an Associated Press count. The AP count of US deaths is six less than the Defence Department's tally. At least 1,484 US military service members have died in Afghanistan as a result of hostile action, according to the military's numbers.
More than 2800 troops from all nations have died since the start of the war in Afghanistan. There are about 130,000 troops from 50 countries serving with the international military coalition.
The Helmand deaths would be the biggest loss of life for Britain in a single incident in Afghanistan since a Nimrod aircraft crashed in 2006, killing 14 service members. It would also be the largest number of casualties in a ground operation for Britain in the country and the deadliest single incident for NATO since January 19, when six US Marines died in a helicopter crash in Helmand province. Last August, insurgents shot down a Chinook helicopter, killing 30 American troops.
The circumstances of the explosion that killed the six British troops were unclear.
"The six soldiers, five from the 3rd Battalion the Yorkshire Regiment and one from the 1st Battalion The Duke of Lancaster's, were on patrol in a Warrior armored fighting vehicle when it was caught in an explosion in the Task Force Helmand area of operations," said Lt. Colonel Gordon Mackenzie, a spokesman for the British Task Force in Helmand. The British defense ministry said the families of the British soldiers have been informed.
Helmand's deputy provincial police chief, Kamaluddin Sherzai, said the incident happened while the troops were on patrol outside Lashgar Gah city. He said they were about 25km east of Lashkar Gah, the provincial capital.
Afghan National Army Major Rahim Ali Almas, who was at the scene on Wednesday as recovery vehicles tried to remove the destroyed tank in the distance, told the AP that the vehicle apparently hit a mine.
"Last night a patrolling convoy ... hit a roadside mine and one of the foreigners' tanks hit the mine and a number of their soldiers were killed." Almas told an AP videographer at the scene.
Cameron said that troops in Afghanistan were paying a huge price. "I do believe it's important work for our national security right here at home but of course this work will increasingly be carried out by Afghan soldiers and we all want to see that transition take place."
NATO has slowly been transitioning security control over Afghan cities and provinces to the country's security forces - which it has spent billions of dollars to train and equip. That transition will be complete at the of 2014.
After the US, Britain has the largest contingent in the international force and says it will withdraw several hundred this year and almost all of them by the end of 2014. The United States has been slowly drawing down its troop presence from a high of about 100,000 in 2011 to 68,000 at the end of summer.
Cameron told the House of Commons that he will discuss with President Barack Obama in Washington next week plans to withdraw almost all international forces by the end of 2014, but stressed that Britain and the US remain in "lockstep" over the proposed drawdown.
He also acknowledged the need to remind the British public why Britain was continuing to bear the burden of military casualties in Afghanistan. "We need to restate clearly why we are there, why it's in our national interest," he said.
On Tuesday, Obama said the accidental burning of Qurans in Afghanistan on Feb. 20 and the retaliatory killings of six US troops by Afghan security forces have given new credence to the need to end the war.
"I think that it is an indication of the challenges in that environment, and it's an indication that now is the time for us to transition," Obama said during a White House news conference.
Obama announced no speeding up of the NATO-backed plan to end combat missions in Afghanistan at the end of 2014, saying "that continues to be the plan." But he said the violence aimed at Americans in Afghanistan that followed the accidental burning of Qurans on a US base was "unacceptable."
He offered his apologies to Karzai, a move that was roundly criticized by his Republican presidential rivals as weak and unnecessary. A letter calling for Obama to accelerate the withdrawal of US troops from Afghanistan had the backing of 23 senators, mostly Democrats but including two conservative Republicans.
