A bishop specialising in safeguarding has said other people in the Church of England might need to quit following the Archbishop of Canterbury’s resignation over an abuse scandal.

Bishop of Birkenhead Julie Conalty, who is deputy lead bishop for safeguarding, said Justin Welby’s resignation alone “is not going to solve the problem”, as she spoke of the need for “institutional changes”.

Mr Welby said on Tuesday that his decision to step down – which came after days of pressure following a damning report into abuse cover-up – was in the best interests of the Church.

Victims of John Smyth, a barrister who led Christian summer camps and is thought to be the most prolific abuser associated with the Church, have called for further resignations from senior clergy members involved in the scandal.

But the second most senior figure in the Church of England has said he does not think any more bishops should resign in the wake of the independent Makin Review into Smyth’s abuse.

Asked on BBC Radio 4’s Today programme about the possibility of more resignations, Archbishop of York Stephen Cottrell said: “Those who actively covered this up (should resign), which was not bishops.

“When people speak about the Church of England, we need to remember we are speaking about literally thousands of branches, parishes, chaplaincies.”

Questioned whether more bishops should resign, he said: “The Archbishop of Canterbury has resigned.”

Asked if that is enough, he added: “Yes, because he has resigned for the institutional failings.”

Keith Makin, who led the independent review, said last week that “despite the efforts of some individuals to bring the abuse to the attention of authorities, the responses by the Church of England and others were wholly ineffective and amounted to a cover-up”.

This is about institutional changes... Very possibly some other people should go. I’m not here to name names

Ms Conalty, speaking on Wednesday, said while Mr Welby has “done the right thing” in resigning, that alone will not solve the Church’s problems.

She told Today: “This is about institutional changes, our culture and a systemic failure, so there must be more that we need to do.

“Very possibly some other people should go. I’m not here to name names.”

Dr Helen-Ann Hartley, the only bishop who had publicly called for the Archbishop of Canterbury to resign, echoed this view.

The Bishop of Newcastle said Mr Welby was “right” to step down, but that it “does not solve the church’s profound failure” on safeguarding “nor does it excuse others whose neglect of their duties is exposed by the Makin report”.

She noted that while some progress has been made in changing the safeguarding culture in the church, “sadly the progress made by many is being undermined by the arrogance of a few”.

Health Secretary Wes Streeting, who said he was speaking “as an Anglican, not as a Government minister”, said it was “absolutely the right decision” for Mr Welby to resign, but church leaders should not think “one head rolling solves the problem”.

He told the Today programme there are “deep and fundamental issues of not just practice, but culture on safeguarding that needs to be taken seriously”.

In his resignation statement, Mr Welby said he was quitting “in sorrow with all victims and survivors of abuse” and that the past few days had “renewed my long-felt and profound sense of shame at the historic safeguarding failures of the Church of England”.

The review concluded that Smyth might have been brought to justice had the Archbishop formally reported him to police in 2013.

Across five decades in three different countries and involving as many as 130 boys and young men in the UK and Africa, Smyth is said to have subjected his victims to traumatic physical, sexual, psychological and spiritual attacks, permanently marking their lives.

He died aged 75 in Cape Town in 2018 while under investigation by Hampshire Police, and was “never brought to justice for the abuse”, the review said.

Bishop of Lincoln Stephen Conway was Bishop of Ely in 2013 when he was told details of Smyth’s abuse.

He has said he “made a detailed disclosure to Lambeth Palace and contacted the relevant diocese in South Africa to alert them to the issue”, and understood it had been reported to police in the UK.

He insisted he “did all within my authority as a bishop of the Church of England” but added: “I acknowledge fully that my fault was in not rigorously pursuing Lambeth about that province-to-province communication, and for this I am deeply sorry.”