The chair of a House of Lords committee has said the number of bishops in the Lords should fall after the National Secular Society criticised its proposals for reform.

Lord Burns, who chairs the Lord Speaker's committee on the size of the House, told the Sunday Telegraph the committee favoured a reduction. He said it had excluded the measure from a report last week because it would have been a "distraction".

The committee, which had members from all parties and the crossbenches, said the Lords should be reduced to 600 members and its size capped at that number. It only suggested changes which would not require legislation after the Government ruled out passing it. It did not consider recommending reducing the number of bishops in the Lords, as the measure was outside its remit.

The NSS criticised the proposals on the basis they would hand bishops more power.

This weekend Lord Burns told the Sunday Telegraph he accepted the number of bishops in House of Lords should be cut in line with that of ordinary peers.

"The underlying view of the committee was it would be better if there was a reduction in numbers," he said. However, he added: "whether there are 26 bishops or 16 bishops does not change the nature of this House. There's plenty of time for that.

"The most important thing is to get the major structure in place. We can then worry about some of the other issues at a later point.

"It's slightly anomalous that the result of this will be that the share of the bishops is larger, the share of the hereditaries is larger, but we can live with that, certainly for a period."

In response NSS campaigns director Stephen Evans said: "The Church of England's privileged power to shape UK legislation needs to be curtailed, and sooner rather than later.

"It is unclear why reducing the number of bishops would be a distraction, why this issue should wait for a later date, or why an increase in the bishops' power can be tolerated for a period. Lord Burns's defensive language appears designed to obfuscate the issue.

"And the power to take significant action lies with the Government. A meaningful public debate on the bishops' place in the Lords is overdue, and should conclude with the decision to remove their automatic right to sit in the UK parliament."

In its submission to the inquiry earlier this year the NSS urged the Committee to consider entirely removing the Bishops' Bench and ending the arrangement whereby religious representatives are given seats as of right. It argued that the bench is "an anomaly in a modern, liberal democracy and if a need to reduce the size of the chamber has been identified the Bishops' Bench is an obvious place to start".

A Church of England spokesman said David Urquhart, the Bishop of Birmingham and convenor of the Lords Spiritual, had "warmly welcomed" the report as "a clear way forward for dealing with the problem of the size of the House of Lords".

Bishop Urquhart "has said that bishops would not be averse to discussing the issue in principle", but "ultimately it is for Parliament to decide what shape reform of the Lords should take, and what the role of the bishops is within that".

A poll commissioned in 2010 by the Joseph Rowntree Reform Trust found that 74% of the population – including 70% of Christians – believe it is wrong that some Church of England bishops are given an automatic seat in the House of Lords.

Discuss this on Facebook.