A radical change to the voting system at Westminster, entailing parliamentary bills being passed in a more proportional way, should be introduced to resolve the row over English-only laws, the Liberal Democrats will say on Friday.

In a Guardian article, the Lib Dem minister David Laws calls on the Tories to follow the example of the Labour party in setting aside “narrow partisan interest” to resolve the matter.

The intervention by Laws comes as a fresh coalition row flared up after Nick Clegg accused Theresa May of making “false and outrageous” slurs against his party. She had claimed the Lib Dems were putting children’s lives at risk by blocking surveillance legislation, known by critics as the snooper’s charter.

Speaking on his Call Clegg radio show, the deputy prime minister said it was dangerously irresponsible of May to have blamed the Lib Dems for risking lives when she promised that the Tories would revive plans to give security services and police more internet snooping powers.

“To say I’ve put children at risk is a level of misinformation I’ve not witnessed in four and a half years of this government,” Clegg said as he confirmed that he had written to the home secretary demanding an apology, warning that coalition relations were now at a low point.

The Lib Dems are also angry with the Tories following David Cameron’s apparent suggestion, after the Scottish referendum, that further powers to Holyrood would depend on ensuring that English-only law at Westminster was enacted in a fairer way.

The party said the prime minister’s statement appeared to breach the cross-party “vow”, issued during the referendum campaign by Clegg, Cameron and Ed Miliband, that further powers would be devolved to Holyrood.

Downing Street subsequently confirmed that extra powers would be granted regardless of changes on English-only votes at Westminster.

But the prime minister, who has appointed a coalition cabinet committee to draw up proposals, issued a new “vow” to the people of England in his speech to the Tory conference to resolve the “West Lothian question” (which queries Scots MPs voting on laws affecting education and health in England only while English MPs get no say north of the border).

Cameron said in his conference speech on Wednesday: “So this is my vow – English votes for English laws. The Conservatives will deliver it.”

The Lib Dems say that the Tories, who would be able to govern on their own in England on the basis of their MPs, should set aside party interest and focus on a fairer system of English legislation.

In his article Laws says that a grand committee of MPs, whose membership would be appointed in proportion to the vote share of parties at the last election, should get the power to veto draft legislation on England.

The composition of parliamentary committees is at present decided in proportion to the number of MPs elected for each party. This would give the Tories a majority on an English-only committee because they have 298 of the 533 MPs elected in England.

The Laws plan would deprive the Tories of a majority, because they secured 39.6% of the vote in England at the 2010 election. The Lib Dems, who won 24.2% of the vote in England, could form a majority on the committee with the Tories or with Labour, which won 28.1% of the vote in England.

The Lib Dem minister says his proposal is entirely consistent with the way power was devolved in the late 1990s to Wales, Scotland and Northern Ireland, where representatives are elected on a proportional system.

Laws, who endorses Labour’s call for a constitutional convention to consider the matter, writes: “It is essential we do this in the right way. Every time Westminster has devolved powers in the past – to Scotland, Wales, Northern Ireland and even London – it has insisted that the devolved authority that wields those powers be put together on the basis of proportional representation.

“This was done not because Labour or the Conservatives have any great love for fair votes. Far from it. It was done because the architects of those devolution settlements understood that allowing one party to have an absolute majority in any new body with a mere 40% or even 35% of the vote would de-legitimise it from the start.

“What was right for Scotland, Wales, Northern Ireland and London is also right for England. Any new body charged with giving English MPs a veto over English laws but must reflect the votes cast for each party in England at the previous general election. That is the only way to ensure it truly represents English opinion and is seen as legitimate by the people of England.

“To do otherwise would be to allow for the possibility that a future coalition government, which received a majority of votes in both the UK and in England, could have its legislative agenda blocked by a party which secured little more than a third of English votes.”

Laws called on the Tories to follow the example of the Labour party. He writes: “No doubt some in the Conservative party would like to introduce a new process which gave them a significant inbuilt party advantage, based on the quirk of constituency results in England. But to do so would be to ride roughshod over the views of the many voters across England – a majority in every general election in my lifetime – who voted for parties other than the Conservative.

“It is to the last Labour government’s credit that they put aside narrow partisan interest when renewing our constitution. The Conservatives must now do the same.”