|Christopher MacManus, one of the hostages|
The Italian prime minister was informed of the deaths by David Cameron in a personal phone call. The British hostage has been named as Chris McManus; he was taken hostage with his colleague, an Italian national, Franco Lamolinara.
In a statement the prime minister said that the hostages were captured in May 2011 and that it was believed the lives of both men were in danger.
Mr Cameron said: "The terrorists holding the two hostages made very clear threats to take their lives, including in a video that was posted on the internet.
"After months of not knowing where they were being held, we received credible information about their location. A window of opportunity arose to secure their release. "We also had reason to believe that their lives were under imminent and growing danger.
"Preparations were made to mount an operation to attempt to rescue Chris and Franco. Together with the Nigerian Government, today I authorised it to go ahead, with UK support.
"It is with great regret that I have to say that both Chris and Franco have lost their lives.
"We are still awaiting confirmation of the details, but the early indications are clear that both men were murdered by their captors, before they could be rescued."