The bodies of two Britons killed while trying to help people evacuate from fierce fighting in Ukraine have been recovered in a prisoner swap, Kyiv officials said on Saturday.

Chris Parry, 28, and Andrew Bagshaw, 47, were undertaking voluntary work in Soledar, in the Donetsk region of Ukraine, when their vehicle was reportedly hit by a shell.

The two were returned to Ukraine authorities as part of a wider exchange, in which Kyiv got 116 prisoners and Russia 63.

"We managed to return the bodies of the dead foreign volunteers," said President Volodymyr Zelensky's chief of staff Andriy Yermak, naming them as the two British men.

Bagshaw was a scientific researcher in genetics but had volunteered as an aid worker in Ukraine since last April.

His remains are expected to be returned to New Zealand where he and his family lived.

The Parry family said he had previously worked as a software engineer.

Concern had grown about their fates after the head of the Russian mercenary group Wagner, which helped capture Soledar from Ukrainian forces, said on January 11 that one of the missing men's bodies had been found there.

Wagner boss Yevgeny Prigozhin had also published online photographs of passports that appeared to belong to Parry and Bagshaw, which he claimed were found with the corpses.