Ken Jones, 50, said: “The family are suffering. We’re just trying to come to terms with it.
“We were prepared for this last night after the Foreign Office phoned us. The family were warned.”
Speaking from the family home in Walton, Liverpool, he added: “Ken’s mum Lily is suffering. We have prepared the family as best we can.
“Lily has not been allowed to watch TV and they will not be seeing the newspapers but at some stage they are going to have to come to terms with what has happened.”
Mr Jones said Mr Bigley’s brother Philip has been “turning greyer and greyer by the day”.
Mr Jones said Mr Bigley’s son Craig had left his pregnant wife at home in Oxfordshire yesterday to be in Liverpool.
He added: “The whole thing stinks. The people who did this are animals, they are barbaric, worse than animals.”
The family’s worst nightmare was realised when militants released a video showing their hostage being beheaded.
The news provoked despair and anger from Mr Bigley’s Netherlands-based brother Paul.
He accused Prime Minister Tony Blair of having “blood on his hands”.
But the rest of the family in Mr Bigley’s home city of Liverpool appeared to back the British Government’s efforts in an “impossible situation”.
The video showed six hooded and armed men standing behind the kneeling hostage, whom witnesses recognised as Mr Bigley from two previous tapes released by the kidnappers.
One of the six then spoke in Arabic for about a minute.
Before committing the murder, the killer said they planned to carry out “the sentence of execution against this hostage” because the British government “did not meet our demand” to release Iraqi women detained by US-led forces in Iraq.
Then the speaker took a knife from his belt and severed Mr Bigley’s head as three others held him down.
Mr Bigley appeared to plead for his life as he was being killed. The recording ended with the killer holding up the severed head.
Mr Bigley’s older brother Stan choked back tears as he told reporters at a press conference in Liverpool: “We will pray for Ken and the families of (fellow hostages) Eugene Armstrong and Jack Hensley.”
British Foreign Secretary Jack Straw last night condemned Mr Bigley’s killing as “barbaric murder”.
He said in a statement: “Now that this terrible news has been confirmed I want to offer the family and friends of Kenneth Bigley my deepest condolences.
“This is a barbaric murder following three weeks of terrible suffering for his family.”