The British deaths came as gunmen in the east abducted 16 mine-clearing personnel working for the United Nations.
A soldier from the 1st Battalion Welsh Guards died in an explosion while on a foot patrol near Gereshk in Helmand province Sunday, the Ministry of Defense said. In the same area Saturday, a rocket-propelled grenade killed one soldier and a roadside bomb killed another soldier, the British Defense Ministry said Sunday.
A total of 174 British personnel have died in Afghanistan since 2001.
The attacks underscore the dangers that the militarily superior foreign troops face in the Afghan countryside, known for its suspicion of foreigners.
The region is a known insurgent redoubt, and since Tuesday it has been the scene of the biggest American military offensive since 2001, when the U.S.-led coalition ousted the Taliban-led government.
It wasn't clear if the British casualties had been involved in the Marine operation taking place farther south in Helmand. Taliban militants frequently use roadside bombs in their fight against Afghan and foreign forces in the country.
Adm. Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, said the Helmand offensive is "the first significant one" since President Barack Obama has ordered 21,000 additional troops to Afghanistan to try to reverse the militant gains.
"We've made some advances early. But I suspect it's going to be tough for a while," Mullen told CBS News' "Face the Nation" on Sunday.
The admiral described the goal of Marines' push as not just driving out the Taliban from areas they control, but securing the area to allow the Afghan government to operate.
"We've got to move to a point where there's security ... so that the Afghan people can get goods and services consistently from their government," Mullen said.
Obama's administration expects the total number of U.S. forces there to reach 68,000 by year's end. That is double the number of troops in Afghanistan in 2008 but still half as many as are now in Iraq.
In the country's east, meanwhile, gunmen kidnapped 16 Afghan mine clearers as they traveled between Paktia and Khost provinces on Saturday, said Paktia's police chief Azizullah Wardak.
While insurgents operate in the area, Wardak could not say who was responsible for the kidnapping. Similar incidents have happened twice before in Paktia but were resolved successfully, he said.
Wardak criticized the demining team - part of the U.N.'s effort to rid the country of decades of planted land mines - for going into the area without informing the police.
Afghanistan is one of the most heavily mined countries in the world, and the increase in violence amid a thriving Taliban insurgency has slowed clearance work. Some 50 people are killed and maimed by mines every month.