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The government has officially withdrawn proposed legislation for elections to the House of Lords after admitting defeat over the plans last month.

In a statement to the Commons, Deputy Prime Minister Nick Clegg said ministers had sought but failed to build a consensus on the changes.

Tory MPs who opposed the plans cheered Mr Clegg as he confirmed the U-turn on the first day after the recess.

Labour said it "shared the coalition's disappointment" about lack of progress.

The government was forced to abandon moves towards a largely elected Lords, championed by the Lib Dems, after nearly 100 Conservative MPs refused to support the plans.

This led to a row between the Conservatives and the Lib Dems, with Mr Clegg accusing Prime Minister David Cameron of refusing to deliver on a key part of the parties' coalition agreement.

Mr Clegg told MPs he "regretted" the failure to reach agreement but the case for a democratic Lords was still overwhelming and he "hoped to return" to the issue after the next election, scheduled for 2015.

He repeated his intention to vote against the implementation of changes to MPs' constituency boundaries, saying reform to the Lords and the Commons were part of the same "constitutional package".

The proposals - strongly backed by the Conservatives - have already been approved in principle by Parliament but Mr Clegg said the coalition partners could not take a "pick and mix approach" to political reforms.

There was no commitment to introduce the boundary changes in time for the 2015 election, Mr Clegg argued, and the Lib Dems as a whole would not support their introduction before then in any future vote.

Without Lib Dem support - and with Labour also opposed - the government would lose any vote, he said.

"The end result is now a foregone conclusion," he told MPs. "The boundary changes will not go through before 2015."

Tory MP Bernard Jenkin said this was "disgraceful", as the redrawing of constituency boundaries - which would reduce the number of MPs by 50 and equalize constituency sizes - was not linked at all to Lords reform.

And Downing Street said it was still the prime minister's intention to have a Commons vote on boundary changes next year.

"It is the law," a spokesman said. "An Act of Parliament sets out the process. The Boundary Commissions are doing their work, they will report next year and after that there will be a vote in Parliament. That vote is required by the act."

Addressing MPs, Mr Clegg also said he would not support separate proposals put forward on the Lords by Lib Dem peer Lord Steel to make it easier for peers to retire and to be stripped of their membership for non-attendance.

He said these would not have the desired effect of reducing the size of the Lords and were "no surrogate for democracy".

For Labour, deputy leader Harriet Harman said Lords reform was "unfinished business" but criticised the government for failing to win over those with genuine concerns on all sides.