Two gay clergy who have earned rebukes from their bishops for marrying their partners have welcomed remarks by Lord Fowler, former chairman of the Conservative Party, criticising the Church of England over its policy on gay marriage.

Lord Fowler said in the House of Lords that the government should be able to stop the Church of England from removing a clergy licence, or permission to officiate, over the issue.

He referred to Canon Jeremy Pemberton, who married his partner in April. Canon Pemberton, a chaplain for the United Lincolnsire Hospital Trust, has been allowed to carry on working in his present job and has merely received a rebuke from the Bishop of Lincoln.

But in the diocese of Southwell and Nottingham, where he actually lived, his permission to officiate was withdrawn by the acting bishop after he married his partner. This means he cannot be given a licence by the acting bishop for a new more senior hospital chaplaincy post he applied for and has been offered in his home diocese.

Canon Pemberton told Christian Today: "I have not lost anything in the diocese of Lincoln. I have a licence from the Bishop of Lincoln. He has given me a rebuke. That is the end of it. However, in Southwell and Nottingham the bishop removed my permission to officiate." He sometimes gets called on by other clergy to help out at Christmas and other services, which he now will be unable to do.

He said: "I am grateful to Lord Fowler for raising it. It is a matter of public interest. The Church of England is the established Church. How it relates to the law of the land is a matter of interest to everybody. It looks very bad to have a church which says we are all right, because we have got exemptions from treating people in a decent way. It looks worse and worse, the longer it goes on."

Father Andrew Cain, a vicar in the London diocese who has also married his partner, has also been rebuked. He also welcomed Lord Fowler's remarks. "I think it would be wonderful if the government would step in and talk sense to the Church of England. It is the state church and it is arguing for exemptions from equality legislation that applies to everyone else. It does rather undermine our right to speak to the government on other moral issues when we behave so badly to gay and lesbian people."

Addressing equalities minister Baroness Northover on the Marriage (Same Sex Couples) Act 2013, Lord Fowler said: "Canon Jeremy Pemberton married his partner in April, as a result of which he has had his permission to work as a priest in Nottinghamshire revoked and been banned from seeking a new post as a chaplain and bereavement manager. Given that there are other clergymen at similar risk, will the Minister, as a matter of goodwill, look at the position and see whether anything can be done to help reconcile the difficulties?"

Baroness Northover replied: "I was a guest at a same-sex marriage very recently and found it extremely moving. The couple had had to overcome so many hurdles to get to a point that so many of us simply take for granted. My noble friend will know that the Bill sought to protect the position of religious organisations and that this is a matter for the Church of England. We hear what he says, and it is worth also bearing in mind that things can evolve. For example, it is good that we should soon see women bishops."

The Bishop of Sheffield, Steven Croft, said: "According to both the letter and the spirit of the legislation on same-sex marriage, it is for the Church of England and all faith communities to determine their doctrine and what is appropriate conduct for their clergy." He said that the recent guidelines of the House of Bishops state clearly that those who enter a same-sex marriage, together with children in their care, should be welcomed into the life of worshiping communities, and also that the Church of England is about to begin a two-year process of structured conversations to explore the changing attitudes to human sexuality and their implications for the life of the church and its disciplines.