Conservative former minister Sir Gavin Williamson said he is more radical on House of Lords reform than the Labour Party, as he urged the Government to be more ambitious in its Bill.

Sir Gavin encouraged Paymaster General Nick Thomas-Symonds to include further changes in the planned reforms. The current Bill, which is getting its second reading on Tuesday, would see the abolition of 92 seats reserved for hereditary peers in the upper chamber.

However, the former education secretary and chief whip said he was unsure whether Labour’s plans to bring in a mandatory retirement age of 80 would ever happen, and asked why 26 Anglican bishops continued to have a role in the Lords.

He told the Commons: “As an Anglican you could say they are representing me well. But I think it’s fundamentally wrong that my children who are Catholics have no form of representation in that chamber. But this Government will not eradicate this injustice.

“There is a big opportunity here, there is an unfairness, there is an injustice. There’s so many people of so many faiths, and so many people of no faith at all.

“See the fact that there are 26 bishops, those are not reflective of the United Kingdom and they’re not reflective of what this country looks like today, but they are still there.”

He later added: “He will equally know that he will not get many opportunities to bring forward legislation in terms of the House of Lords, indeed I would expect this to be the one and only time he gets to bring forward legislation.”

Sir Gavin taunted Mr Thomas-Symonds and urged him to be more of a radical, joking that if he did so, the cabinet minister – who is a published historian on the Labour Party – would find himself the topic of one of his own books.

“He has the potential to be known as a great reformer of the Labour Party. He’ll write books about himself in future, but he needs to be brave, he needs to be bold,” he said.

Brandishing a copy of the Labour Party’s election manifesto, under which it won a 174-seat majority in July, Sir Gavin said Labour’s Bill would not fulfil the promised pledges and instead he would put forward an amendment that would do so.

“I want to see this delivered,” the MP for Stone, Great Wyrley and Penkridge said, tapping on his copy of the manifesto.

“He knows that he will not have an opportunity to bring legislation forward for this again, but … he has an opportunity to make a difference because the things that have been mentioned in their manifesto can be delivered within the scope of the Bill.

“The burning radicalism within his stomach is there that he wants to make a difference, actually I seem to be more committed to delivering this than he actually does.”

SNP deputy leader in Westminster Pete Wishart briefly intervened on Sir Gavin, urging the speaker to “make him stop this inconsequential nonsense”, to which the Conservative MP said he looked forward to “another inconsequential speech” from Mr Wishart later.

The Perth and Kinross-shire MP went on to compare peers to the Baratheons and Targaryens from Game Of Thrones, and described the House of Lords as a “red leather-upholstered, gold-plated Narnia”.

He told MPs: “The first thing you’ve got to try and not do when you consider this Bill is to try not to laugh. Not to laugh out loud at the sheer ridiculousness of considering, in 2024, whether places should be reserved in our legislature for a curious subset of a particular class of person based on birthright.”

He later added: “I suppose in some sort of way, they’re our own Baratheons and Targaryens, only without the fun, without the dragons and the box office appeal. But it’s now time to break the wheel. For them down the corridor there, winter must be coming.”

“That is why I am so proud that my party will never put anybody in that red leather-upholstered, gold-plated Narnia,” he went on to say.

Conservative former minister Richard Holden said he supported the principle of removing hereditary peers, but “as part of a broader package of measures”.

The Basildon and Billericay MP also argued that peers should have a mandatory retirement age, as judges do.

He said: “I would be quite interested to hear from the Government front bench as to how they can justify a mandatory retirement age of 75 for those who interpret the law, but not having a mandatory retirement age for those who make the law.”

Reform UK deputy leader Richard Tice said he was a “big fan of reform” of the House of Lords and urged the Government to “get on with it”.