The Bishop of Chichester, the Right Rev Eric Kemp, said there was 'a general perception that the Archbishop of Canterbury is doing much less (to ensure) that opponents will have a welcome and honoured place within the Church of England' than the Archbishop of York, Dr John Habgood.
Hundreds of Anglo-Catholic priests may leave the Church of England for Rome if they cannot continue in communion with like-minded bishops who refuse to ordain women.
Dr Carey said last week that 'people who abandon positions because their own particular point of view is not upheld by the archbishop or someone else - I don't think they realise they are doing very serious damage to the Christian faith'.
Dr Kemp refused to be drawn on whether Dr Carey should give a clearer lead. He told the BBC: 'I'm not quite sure whether it would be right for Dr Carey to make public statements about it at the moment.'