The remains of two bodies were passed to Britain by the Iraqi authorities late last night.
Foreign Secretary David Miliband said the UK did not yet have confirmation about who they were.
He said the government's thoughts were with the families of five British people taken hostage in Iraq in May 2007.
Mr Miliband described the developments as 'distressing'.
He said the Foreign Office was in close touch with the hostages' families and urged the media to 'give them as much space as possible in these very difficult hours and days'.
The Foreign Secretary reiterated Britain's call for the immediate safe release of 'all the remaining hostages'.
