He added that such actions "in Iraq or elsewhere should not prevail".
Home secretary Jack Straw called the killing a "barbaric murder".
Earlier on Friday an Arab TV station reported that Mr Bigley had been killed and said it had been given a video that showed him being killed.
They didn't show that video to anyone, but some journalists working in Iraq said they had seen it and said it appeared to show Mr Bigley being killed.
Mr Bigley was an engineer and was in Iraq to try and help improve the country after the war.
The group which took him doesn't like the Iraqi Government and do not want foreign people in the country.