Government uses rare parliamentary procedure to annul seven adjustments to reform and prevent further challenges from peers

The coalition has raised the stakes over its welfare bill by overturning seven key Lords amendments passed to soften the reforms, and taken the rare step to direct peers they have no constitutional right to challenge the Commons' decisions further.

On most bills, the Lords can send amendments back and forth in what is known as parliamentary ping pong. The coalition, deploying a rarely used parliamentary device, claimed "financial privilege" asserting that only the Commons had the right to make decisions on bills that have large financial implications.

It argued that the Lords amendments collectively cut billions of planned savings. A similar tactic could also be used to throw out likely Lords amendments to the legal aid and health bills.

It is for the Speaker on the advice of clerks and the coalition to decide if financial privilege should be applied.

MPs backed the government's plans for a £26,000 annual cap on overall household benefits including child benefit, overturning a defeat in the Lords. The Lords amendment, which was led by Church of England bishops, was overturned by 334 votes to 251.

The shadow work and pensions secretary, Liam Byrne, said he favoured a regionally based cap, reflecting different housing costs. He refused to say if this would mean the cap would be lower than £26,000 in the north of England.

Labour peers and some crossbenchers argued that the understood convention was that financial privilege only applied to money bills, such as the bill implementing the budget, adding that almost all Lords amendments have some financial consequence for the government.

Lord Hunt of Kings Heath, the deputy leader of Labour peers, said ministers were "hiding behind parliamentary procedure to curtail consideration of the amendments that we passed. If the government continues to do this on these bills, our role as a revising chamber is effectively undermined".

The former lord chancellor, Lord Mackay of Clashfern, who led the Lords rebellion against charging single parents for using the Child Support Agency, said it was a "waste of taxpayers' money at a time of considerable austerity" for peers to pass amendments that were subsequently rejected out of hand.

Lord Strathclyde, the leader of the Lords, said the procedure of invoking financial privilege was "well precedented" and "nothing unusual".

He said: "The matters of privilege are not a matter for the government but a matter for the House of Commons – the Speaker of the House of Commons on advice from his clerks. The position of privilege has been jealously guarded by the House of Commons since 1671."

He added: "I do not think we waste our time in debating these issues. We do not insist on all the amendments we pass in this House. We send them back to the House of Commons to get the government and the House of Commons to think again. If they have thought again and invoked financial privilege I think we should let the matter rest."

In the Commons, Menzies Campbell, the former Liberal Democrat leader, was one of four of his party to rebel over imposing a one year limit on means-tested employment support allowance.

His party conference had voted against an arbitrary time limit in the autumn, but Jenny Willott, the party's social security spokeswoman, voted for the one year limit, arguing that the Lords amendment of two years was also arbitrary. She said evidence showed the work capability assessment, the test used to determine if a claimant qualified for ESA, was improving.

Of the Liberal Democrat peers 12 rebelled on the so-called bedroom tax, for cutting benefit over "under-occupied" housing.

However, a nine-month grace period was announced before the £26,000 cap is imposed for someone made unemployed through no fault of their own, and who was in work for the previous 12 months; and a discretionary £80m fund in 2013/14.

Grayling said: "There is agreement that it is wrong to pay people who do not work more in benefits than people earn on average when they work. The cap sets a firm upper limit to total benefit entitlement which, for families and lone parents, will be equivalent to the average wage for working households".

At Prime Minister's Question Time David Cameron repeatedly challenged Labour to support the threshold, saying: "The cap is right and the cap is fair."

Grayling said the public "overwhelmingly" supported the Government's stance and accused Labour of being guilty of "flip-flopping" on the issue, initially supporting a benefits ceiling before the party's peers supported an amendment in the Lords to exclude child benefit from any cap.

The Government also said it would not make any changes to its proposals to force those living in council houses that were bigger than they needed, to move.

The Lords had proposed social landlords could only force a tenant to move to a smaller home if a social landlord could offer alternative accommodation, which was supported in the Commons by Lib Dem deputy party leader Simon Hughes.

But the employment minister Maria Miller said the changes were needed to relieve the pressure on social housing and free up one million empty free rooms to help families in over-crowded accommodation. She said the average cost of the measure would be £14 a week.

In other reforms reimposed by MPs in six hours of debate: people who are recovering from an illness or injury will get contributory Employment and Support Allowance for one year, half the period that the Lords decided.

The limit would also apply to some cancer patients, despite moves by peers to exempt sufferers from the time limit.