"Without this British special forces soldier, many more lives would have been lost," the Daily Mirror quoted a senior British military source as saying.

"His selfless action will be remembered by those he rescued and privately celebrated and acknowledged by his colleagues," the military source said.

The paper said the man was part of a small "liaison" team embedded with Kenyan special forces.

Former special forces soldier Chris Ryan was quoted in the paper as saying the man was "out shopping" when the attack started.

The Times said he is a "long-serving member" of Britain's elite SAS (Special Air Service).

Pictures of the man, who wore jeans, a purple jumper and a balaclava, showed him rescuing survivors. He was wearing body armour, holding an assault rifle and carrying a pistol.

The British government does not comment on special forces.

Five gunmen with the Al-Qaeda-linked Somali militant group Al-Shabaab attacked the DusitD2 hotel and office complex in Nairobi on Tuesday, killing 21 people.

Kenya on Wednesday said the attack was over and all five assailants were dead.