The Ministry of Defence said it was investigating the circumstances of the crash, and is in the process of contacting next of kin.
It is the first fatal accident involving a UK military helicopter in Afghanistan since the conflict began.
An Afghan official said the helicopter carrying soldiers from the International Security Assistance Force (ISAF) coalition of international forces had crashed due to technical problems.
The crash, near Kandahar air base, in Kandahar province, comes as Nato forces are preparing to withdraw combat troops by the end of the year.
Kandahar provincial police spokesman Zia Durrani said the helicopter went down in the Takhta Pul district, 30 miles from the Pakistan border. He said the helicopter was on a "training flight" and it was unclear why it crashed.
Although the Taliban claimed responsibility, the crash, which makes this the bloodiest day for foreign troops in Afghanistan in 2014, is not thought to have involved any enemy action. The Taliban routinely claim responsibility for all aircraft losses, even those that Nato forces say were due to accidents.
Taliban spokesman Qari Yousaf said the helicopter was on a routine military exercise when Taliban fighters hit it in the Takhta Pul district of Kandahar.
An MoD spokesman said: "We can confirm that a UK helicopter crashed in southern Afghanistan today. The incident is under investigation and it would be inappropriate to comment further until families have been notified."
The helicopter involved is thought to have been a Westland Lynx Mk 9, which is a light utility aircraft used for a range of tasks.
They usually carry a crew of three, including a pilot, co-pilot and gunner.
It is thought that the other two military personnel on board could have been travelling as passengers.
The deaths bring the total number of international troops killed in Afghanistan this month to seven.
Defence analyst Paul Beaver said: "It is difficult to speculate on what has happened, but it sounds like this was a flying accident instead of a case of the aircraft being shot down.
"It could be weather related, it could be dust or it could have been trying to avoid birds, for example, or it could be some kind of mechanical failure. There is a whole range of possible causes."
Beaver said that a board of inquiry would have been set up immediately by the Military Aviation Authority to establish the reasons for the crash.
He said the investigation would look at the aircraft's log books and other documentation, in addition to weather conditions and whether the helicopter was carrying out an authorised job according to its capabilities.
Beaver explained that although Nato troops are gradually withdrawing from Afghanistan they are still involved in military operations.
"The draw down is happening but it does not mean British troops have stopped operations," he said. "This helicopter could have been taking people from one location to another or it could have been inserting or recovering people."
The crash is one of the worst air crashes involving British forces in the country.
Helicopters are used extensively to transport troops in Afghanistan. The last major helicopter crash took place in December killing 11 people when a Blackhawk was shot down by the Taliban.
Isaf said earlier in a statement: "Five International Security Assistance Force service members died as a result of a helicopter crash in southern Afghanistan today.
"Isaf is still in the process of reviewing the circumstances to determine more facts."