He was in a task force sent to save the officer, held hostage by Taliban gunmen.
British and Afghan troops laid siege to a village police checkpoint on Sunday night after deputy chief Abdul Walid was kidnapped there just hours earlier.
The allied raiders snatched terrified Mr Walid from the extremists — but one of the heroes was killed by gunfire in the battle and a British comrade injured.
The dead soldier, of 3rd Battalion, The Yorkshire Regiment, is Britain’s only 417th victim of the conflict. He has not yet been named but his family has been told.
Gulab Mangal said in a statement: “I wish to praise the sacrifices and bravery of UK forces in saving an Afghan police officer. I and the local residents will never forget such sacrifices. We offer our sympathy to the British Government.”
Lt Col John Kerner, of British Forces Helmand, said: “This loss is felt by everyone.”
The Taliban gunmen fled during the firefight but troops seized a mobile phone, valuable documents and explosives.