Peers backed plans for a compromise aimed at ending a row over the Parliamentary Voting System and Constituencies Bill.
Labour opposes plans to cut the number of MPs and redraw constituencies.
Ministers wanted the number of voters in each constituency to be within 5% of around 76,000 – peers backed moves to make that 7.5% in “exceptional” cases.
The bill must become law next week if the government is to meet its deadline for holding the planned referendum on the alternative vote system in May this year.
It paves the way for a referendum on changing the way MPs are elected.
But it also contains plans to cut the size of the House of Commons from 650 to 600 MPs and change the size of parliamentary constituencies, which are opposed by Labour.
The government wants all but two of the constituencies in the Commons to be of equal size, containing about 76,000 voters.
Ministers had proposed that the number could be varied by 5% either way to take account of local circumstances.
WHAT IS ALTERNATIVE VOTE
Under the AV system, voters rank candidates in their constituency in order of preference.
Anyone getting more than 50% of first-preference votes is elected.
If no-one gets 50% of votes, the candidate with the fewest votes is eliminated and their backers’ second choices allocated to those remaining.
This process continues until one candidate has at least 50% of all votes in that round.
Crossbench peer David Pannick QC proposed changing that to 7.5% in an effort to end the political stand-off over the bill. He said the Boundary Commission would only be able to apply the variation in “exceptional circumstances”.
Labour supported the changes, but Conservatives and Liberal Democrats argued against the proposals and the government urged peers to reject the amendment.
But when peers voted the government was defeated by 275 votes to 257, a majority of 18 votes.
On Tuesday the government suffered another defeat when peers backed a plan to make the referendum on the voting system binding only if 40% of the public took part.
MPs must now decide whether to retain the proposal or overturn it when the legislation returns to the Commons.