He adds: 'Just as well, then, that we are surrounded by a large and wonderful family who give us great support and pleasure.'

Carey, who retired from his position in 2002, was forced by Welby to resign as honorary assistant bishop in the diocese of Oxford after a damning independent inquiry criticised his handling of the Ball case. Lord Carey quit after Welby made an unprecedented request for him to 'carefully consider his position'.

The inquiry found that the Church had 'colluded' with Ball, the former bishop of Lewes and Gloucester, 'rather than seeking to help those he had harmed'.

Ball was released from prison in February this year after serving 16 months for the grooming, sexual exploitation and abuse of 18 vulnerable young men who had sought spiritual guidance from him between 1977 and 1992.

The inquiry found that in the case of Ball, the Church 'appears to have been most interested in protecting itself' and that Carey 'set the tone for the church's response to Ball's crimes and gave the steer which allowed Ball's assertions that he was innocent to gain credence'. Carey had failed to pass six letters raising concerns about Ball to police and in 1993 wrote to Ball's twin brother, Bishop Michael Ball, saying: 'I believe him to be basically innocent.'

Following the release of the inquiry's report, Carey apologised to Ball's victims, saying: 'I believed Peter Ball's protestations and gave too little credence to the vulnerable young men and boys behind those allegations.'

Now Lord Carey has hit back over the affair in a Christmas letter from him and his wife, Eileen, to 'our dear friends'.

The letter says 'two things have happened to us of consequence' over the past year: a move to a new home in a retirement community, and the 'less desirable' one was Welby's intervention in June.

The letter follows criticism of Welby over his handling of a separate abuse claim, against the revered George Bell, who was bishop of Chichester until his death in 1958.

On Friday, the Church was heavily criticised for rushing to judgment and traducing Bell without rigorous investigation of the claim, with Welby playing a role in Bell's name being made public.

In a letter to Bell's niece, Carey said he was 'frankly appalled by the way the church authorities have treated his memory'.

He added: 'The church has effectively delivered a "guilty" verdict without anything resembling a fair and open trial,' leaving Bell's reputation 'in tatters'.

A spokesperson for Carey said no comment would be made on private correspondence intended for friends.

A spokesperson for Welby also declined to comment on private correspondence but added that the independent review on the Ball case spoke for itself.