British Foreign Secretary Dominic Raab on Friday said US airstrikes in Iraq were a "proportionate" response to the deaths of two Americans and one Briton in a rocket attack.

The Pentagon said the strikes were against the pro-Iranian Kataeb Hezbollah armed faction in response to the death of the three soldiers on the Taji air base on Wednesday.

"The response to the cowardly attack on coalition forces in Iraq has been swift, decisive and proportionate," Raab said in a statement.

"We will continue working with our partners to ensure those responsible for these deplorable acts will be held to account. 

"UK forces are in Iraq with coalition partners to help the country counter terrorist activity and anyone seeking to harm them can expect a strong response."

The British soldier killed has been named by the defence ministry as Lance Corporal Brodie Gillon, a 26-year-old reservist. 

A self-employed sports physiotherapist in civilian life, she had been working as a combat medical technician.

"She was a larger than life soldier who was determined to deploy on operations, help others, develop herself and gain practical experience," her commanding officer, Lieutenant Colonel William Leek said in a statement. 

"She had already achieved a great deal in her relatively short time with us and it was abundantly clear that she was destined for great things in her civilian and military careers. 

"Her loss is keenly felt."