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MPs have overturned a proposal to make a referendum on the Westminster voting system non-binding unless 40% of the electorate take part in the poll.

Peers backed the measure earlier this month but the Commons rejected the proposal by a majority of 70.

Cabinet Office minister Mark Harper said there was a "compelling" case for voters to make the final decision.

MPs rejected a number of other Lords amendments as they sought to pass a bill needed to enable the referendum.

Ministers said they had listened to concerns from MPs and peers over the bill and "engaged constructively" over the most contentious issues but Labour said the bill was being "bulldozed" through Parliament.

The Parliamentary Voting System and Constituencies Bill has to be approved by Parliament by Wednesday so that it can become law in time to hold the referendum on the Westminster voting system on 5 May as intended by the government.

Aside from enabling the referendum on whether to switch from first-past-the-post to the Alternative Vote, the bill will cut the number of MPs from 650 to 600 and change parliamentary boundaries so that constituency electorates are broadly the same.

Mr Harper said the 40% threshold plan for the referendum would "encourage people to stay at home" and flew in the face of the principle that people "should get what they vote for".

Labour supported the amendment, put forward in the Upper Chamber by Lord Rooker, but the measure was comfortably defeated in a Commons vote. Peers will decide on Wednesday whether to try and reinstate the clause - putting it at odds with the Commons.

MPs also voted to overturn another proposal backed by peers which would have allowed the Boundary Commission to allow constituencies to deviate by up to 7.5% from the proposed standard 76,000 size in exceptional circumstances - as opposed to the 5% supported by the government.

But the government did make a concession to protect the Isle of Wight from some of the boundary changes designed to ensure parliamentary constituencies have roughly the same number of voters.

Under the government's initial plans, the Isle of Wight would have been divided into two constituencies - with one attached to the mainland.

But the plans for a "cross-Solent" seat prompted substantial opposition and the coalition was defeated on the issue in the Lords last month.

The government has decided that the Isle of Wight will be divided into two seats - but within the geographic boundaries of the island - and the plans were approved by MPs.

Mr Harper said ministers were responding to the "strength of opinion" expressed by parliamentarians and the public over the issue.

The two Houses of Parliament must decide on the final wording of the bill on Wednesday if it is to get Royal Assent on Thursday.

For Labour, Chris Bryant said many MPs would "rue the day" on which they approved the bill, given the unsatisfactory way in which it had been conceived and debated.

"The government has bulldozed its way through every convention so far," he said. "This is not legislating on the basis of the long-term democratic health of this country or on the basis of sound principles but solely to meet the partisan needs of the coalition."

A number of Tory MPs also criticised the way in which the legislation had been handled.

Bernard Jenkin, chair of the Public Administration Committee, said it had been passed with "indecent haste" and the referendum campaign would be squeezed into eleven weeks rather than the six months foreseen in past legislation governing such polls.

"This is a shoddy way to conduct a referendum. It is unconstitutional, it is deeply political and it will undermine the value of any referendum result," he said.