The remains of Lucky, Lisa and Alfred Hitch were found on Monday morning on the site in Old Ford, east London.
The security company Group 4 has been criticised recently for the escape of prisoners being transported under its new contract. A spokesman for The Big Breakfast said: 'The Group 4 officers are used to people getting out, not foxes getting in.
'The dead chickens were discovered only when members of the crew realised the garden was too quiet. That was just before we went on air.'
A spokesman for Group 4 said: 'Guarding the chickens was not part of our contract.
'Foxes attack all over the country and there is nothing you can do to guard against it.
'It is no reflection on the competence of our staff. As far as we are aware The Big Breakfast is delighted with the service we provide.'
He added: 'Our guards are as upset as anyone about it. As a gesture we have agreed to replace the chickens with three new ones.'