A spokesman for the Nato-led International Security Assistance Force (ISAF) confirmed that the three killed were British.
Insurgents, armed with rocket-propelled grenade launchers, ambushed an ISAF vehicle north of Helmand province on Tuesday morning.
Britain has nearly 4,000 soldiers deployed in Helmand.
The confirmation of the latest death takes to nine the number of British soldiers killed in Afghanistan this year.
The attack came a day after Nato took command of the south from the US-led coalition, with a mission to stabilise the region.