It supports the call by the UN high commissioner for human rights for an international, independent investigation into violations of human rights and related crimes by both sides during the war.
A vote on resolution will take place at the end of this month.
A spokesperson for the British PrimeMinister added: "Ahead of the vote, we are working hard to secure support from other countries. The PM has personally written to a number of leaders whose countries are on the human rights council this session calling on them to support this resolution which would help to deliver progress on reconciliation and human rights in Sri Lanka."