Plans to restrict the voting rights of Scottish MPs at Westminster have been scrapped after splits emerged in the UK government before September's independence referendum.

Senior sources say the coalition has dropped plans to tackle the so-called West Lothian question because of fears it could fuel Scottish resentment, but also because the Tories and Lib Dems cannot agree on whether voting restrictions on MPs are fair.

Moves to restrict Scottish MPs' votes – by limiting their rights to vote on England-only legislation – have also been fought off by Labour and by senior Lib Dem figures, who plan to increase devolution to major cities and regions within England.

Ed Miliband is to unveil proposals this week to devolve £30bn in funding to English cities and regions if Labour wins the 2015 general election, to increase the spending and policy-making powers of cities such as Manchester and Birmingham. The strategy is due to include housing, the economy and employment policy.

The government is expected to hand major new economic powers as part of Nick Clegg's "city deals" programme to Glasgow, the UK's second-largest city outside London and the first to be given those powers outside England, later this week.

Miliband made clear on a visit to Edinburgh on Friday that he was opposed to any measures that created "second-class MPs". He said the best solution was to increase devolution across the UK, rather than restrict it to Scotland, Wales and Northern Ireland.

A UK cabinet source said there was a wider concern about damaging the "constitutional integrity" of the Commons by creating two tiers of MP which were, a concern shared by some senior Tories and Lib Dems. "The answer to the West Lothian question is not to be found within the walls of Westminster: it comes from proper devolution," he said.

The West Lothian question, posed by the Labour MP for West Lothian Tam Dalyell in 1977, focuses on the ability of Scottish, Welsh and Northern Irish MPs to vote on solely English policies such as health and education, when English backbenchers are unable to vote on those subjects as they are devolved to Cardiff, Edinburgh and Stormont.

In January 2012, after years of complaints about the anomaly from Tory and some Labour MPs, the coalition set up an expert commission under William McKay, a former clerk to the Commons, to reform voting on England-only policy in the Commons.

The commission recommended in March 2013 that English MPs should be given the greatest influence over England-only laws, such as an English grand committee for the main stages of a bill's progress through the Commons or separate votes where elements of a bill were England-only.

The commission published research by the Institute for Public Policy Research which found that 81% of English voters thought Scottish MPs' votes on English matters should be restricted, although only 20% of English voters wanted an English parliament.

Despite that evidence, a UK cabinet source said the Tories and Lib Dems were divided on whether restricting the voting power of Scottish MPs was constitutionally necessary and fair, because it undermined the central principle that every voter's ballot was equal, regardless of where they lived.

"The appetite amongst people living outside London and the south-east is now for meaningful devolution to their communities away from Whitehall," he said. "And there will inevitably follow a process of political accountability.

"From the point of view of the referendum, it's essentially to keep the focus clearly and squarely on the independence question. Discussions in Scotland on other aspects of the constitution risk blurring that focus in a way that's not helpful."