Plans to reform the appointment process of the House of Lords are one step closer to becoming law after several peers from across the political spectrum acknowledged the upper chamber is “too large”.

Sponsored by constitutional expert and Tory peer Lord Norton of Louth, the House of Lords (Peerage Nominations) Bill would strengthen the House of Lords Appointments Commission’s (HOLAC) role by requiring the Prime Minister to wait until the commission had advised on whether a nominated individual met specified criteria.

The principal criteria would be “conspicuous merit” and a “willingness and capacity to contribute to the work of the House of Lords”.

Moving the second reading debate in the upper chamber, Lord Norton complained “recent prime ministers have been rather profligate in making nominations for peerages”.

He added: “Just after the enactment of the House of Lords Act 1999, we were approximately the same size in membership as the House of Commons.

“We now exceed membership of the House of Commons by a three-figure number. We have discussed and agreed without dissent that we are too large.

“The process of nomination is also a matter of contention, the media variously criticising those whose names have been put forward. I’m not concerned today with particular cases but with the problems associated with the process.

“My key concern is achieving an appointment process that merits the trust of the people: this Bill is designed to contribute to achieving that.”

The Bill received an unopposed second reading, as is convention for private members’ bills in the upper house,  and will now undergo further scrutiny at a later stage.

While many peers spoke in favour of the proposals, plans to wreck the Bill will traditionally come to the fore at committee and report stage.

Consideration of proposals follows accusations that former prime minister Boris Johnson has proposed several Conservative MPs for peerages, but told them to delay accepting them to prevent triggering by-elections.

Mr Johnson’s resignation list, alongside Liz Truss’s, could also see a large increase in the number of Tory peers in the House of Lords, at a time when the size of the upper chamber is already seen as being excessive.

Lord Norton argued “there are no formal constraints on whom the Prime Minister can nominate, nor the number of names that can submitted” and that whilst the commission “does a very worthwhile job”, its powers are “limited, not least in terms of scrutiny”.

Detailing his Bill, the Conservative peer said: “It protects the Appointments Commission and its independence by putting it on a statutory basis and providing that members, including the chair, are nominated jointly by the Speaker of the House of Commons and the Lord Speaker.”

Lord Norton explained the Prime Minister would also be required to have regard to three principles when determining whether to recommend individuals for new life peerages.

These would be that at least 20% of the membership of the House of Lords must comprise members who are independent of a registered political party; that no one party may have an absolute majority of members; and that the membership of the House of Lords must be no larger than that of the House of Commons.

Lord Alton of Liverpool, an independent crossbencher, said the Bill was a “no-brainer”, after explaining: “The House of Commons is not a well-run legislative chamber.

“The majority of its members who are not on the payroll vote are not legislators, they are actively discouraged from being legislators, particularly when you have a large majority as of present.

“We do most of the heavy lifting here. As a headhunter the idea of appointing somebody in theory to legislate, but then doing virtually nothing is anathema, it’s perverse, it’s disreputable.”

Meanwhile, Labour peer Lord Howarth of Newport said the “size of the House has grown inordinately with mass appointments of political peers”, adding: “Whatever the individual merits of new colleagues, the scale and partisanship of appointments has damaged both the reputation and the functioning of the Lords.”

Cabinet Office minister Baroness Neville-Rolfe told peers the Government will “of course reflect”on the debate.

However, explaining her reservations about the Bill, she said:  “The Prime Minister is ultimately responsible to Parliament and the people for any nominations that he, or in the past she, makes to this house, and the Government does not see the case for changing this.

“The Government considers, however, that the House of Lords Appointments Commission forms its role well as it’s currently constituted, and is extremely grateful for the work that it does.

“The fact that members of this House are appointed from a wide range of backgrounds is testament to its success.”

Intervening, former Lord Speaker and independent crossbencher Baroness Hayman questioned how Conservative former prime minister Boris Johnson is currently accountable to the British public.

She said: “Could she explain to me how the last but one prime minister Boris Johnson, against whom many of the criticisms about appointments have been made, is in any way now accountable to the British public or to Parliament for what he did?

“We do not have, as someone said, a presidential system, the Prime Minister is not personally accountable for this and all this Bill is trying to do is to ensure a degree of probity and appropriate scrutiny, a check and a balance for which our constitution is so well respected, in the process of appointments to your Lordships’ House.”

The Cabinet Office minister replied: “Our Prime Minister, as she says, becomes accountable… for putting forward the names of peers in the future, taking into account the advice of HOLAC.”