Also on Monday, the US military said fighters shot down a US helicopter during fighting south of Baghdad on Sunday, killing two soldiers.
The incident took place near the town of al-Yusifiya, 15km south of the capital. The area is a stronghold of Sunni Arab fighters battling US forces and the Iraqi government forces they back.
Elsewhere on Monday, four Iraqis were killed and five wounded in two other attacks, including a roadside bomb that hit an oil tanker, sending a large plume of black smoke billowing over central Baghdad.
The mortar barrage on the British military camp occurred at about 4.30am (0030 GMT) at Camp Abu Naji in Amarah, 290km southeast of Baghdad, said British spokeswoman Captain Kelly Goodall.
One of the British soldiers received a serious leg injury, but the other wounds were minor, said Holly Wheeler, a British ministry of defence spokeswoman in London.
The attack raised the total of British casualties in Iraq over the past nine days to six soldiers killed and five wounded.
The attacks all occurred in southern Iraq, an area that has traditionally been far more peaceful than central and northern Iraq where US forces are based.
On Saturday, two British soldiers were killed and one was wounded by a roadside bomb as they patrolled in their armoured vehicle north of Basra city.
Elsewhere on Monday, a drive-by shooting at about 8.30am killed four teachers who were heading to their school in a village near Balad Ruz, a town 80km northeast of Baghdad, police said.
The attackers and those killed were both riding in minibuses, the private vehicles that charge small fees to transport the general public.
In central Baghdad, a roadside bomb directed at a police patrol missed the officers but killed one civilian, wounded four and set fire to an oil tanker parked nearby.
Police Captain Ziyad Naji said: "The explosion caused a huge fire."