Mr. Cameron’s Conservative Party has the most members, 226, or 14 more than the opposition Labour Party. But with many peers not attached to a political party, that leaves the government vulnerable to defeats.

The political lineup is noticeably out of kilter with the results of May’s general election. For example, the centrist Liberal Democrats, who won just eight seats in the House of Commons and 7.9 percent of the vote in May, have 101 seats in the upper chamber.

Despite such anomalies, the assembly survives partly because it knows its place. As an unelected body, the Lords will ultimately yield on legislation if the elected House of Commons so demands. That avoids the type of gridlock sometimes seen in bicameral legislatures in other nations, including the United States.

“One of its virtues is that it is different from the Commons,” said Elizabeth Gibson-Morgan, a constitutional expert who teaches both in France and at King’s College London. “Turning it into an elected house would turn it into a clone of the Commons.”

But even before the latest scandal, there was growing opposition to enlarging the Lords, especially while Mr. Cameron has vowed to trim the House of Commons from 650 members to 600 to “cut the cost of politics.”

Though much less expensive to the taxpayer per seat than the salaried legislators in the Commons, costs in the House of Lords are under scrutiny. According to the Electoral Reform Society report, in the 2010-2015 Parliament, peers who failed to vote even once in some years claimed a total of £360,000 in allowances, and the appointment of an additional 50 members would cost “at least £1.3 million per year.”

Kirsty Blackman, a member of the Scottish National Party who was recently elected to the House of Commons, described the House of Lords as bloated, outdated, undemocratic and a “horrendous waste of money.”