Ministers are to set up an expert inquiry into limiting the voting rights of Scottish, Welsh and Northern Irish MPs at Westminster, the government has confirmed.

The commission into the so-called West Lothian question will look into long-running complaints about the continuing right of MPs from parts of the UK with their own parliaments or assemblies to vote on legislation affecting only England.

Mark Harper, a junior Cabinet Office minister, said the panel of "non-partisan" academic experts on the constitution, the law and parliament would investigate how England-only laws are handled by both the Commons and the Lords, now that there are devolved legislatures in Cardiff, Edinburgh and Belfast.

Backbench MPs in the main UK parties have stepped up their complaints about the anomaly at Westminster where Scottish, Welsh and Northern Irish MPs can still vote on issues such as health, policing and education issues when they are onlyrelevant to England.

Many non-English backbenchers, particularly nationalist MPs in the Scottish National party and Plaid Cymru, voluntarily often avoid votes on England-only legislation except on controversial measures or on bills which have a significant financial impact on their countries.

Michael Moore, the Scottish secretary, said: "We understand how exercised colleagues in England are but if there was a simple solution to this, it might have been found some years ago but we will endeavour to do this because it has been ignored for a very long time."

The West Lothian question was first posed by Tam Dalyell, then MP for West Lothian during a debate about devolution in 1977.

It is regarded as one of the most serious anomalies of devolution, with control over most major domestic policies in Scotland, Wales and Northern Ireland now solely in the hands of the devolved parliaments and assemblies.

Successive governments have played down its significance because they feared it would play into the hands of nationalist parties by weakening ties to the UK parliament, and diluting the influence of Scotland, Wales and Northern Ireland at Westminster. It could also accelerate pressure for a more federal structure for the UK.

Even so, the UK government promised to set up a commission on the West Lothian question as part of their coalition agreement in May last year, chiefly under pressure from the Tories. The government had been expecting to make a formal announcement on the commission's remit and membership after the October recess. It will publish the final details about its scope later this year.

UK ministers were forced into an early announcement on Thursday to block a private member's bill from the Tory backbencher Harriett Baldwin, the MP for West Worcestershire, which seeks to limit voting rights at Westminster, and has unexpectedly passed a series of hurdles in the Commons.

Baldwin's bill, which is not supported by the UK government, is due to complete its passage of the Commons on Friday and would then go to the Lords. It would require ministers to state on each bill whether it only affected England, to put non-English MPs under pressure not to vote on it.

Baldwin said she wanted to study Harper's statement before deciding whether she would drop the legislation (territorial extent) bill and allow the issue to be studied by the commission instead.

Harper said the commission would not study the financial impact of devolution because of existing work by Treasury ministers, nor would it question the number of MPs sitting in the Commons. This issue was already being addressed by existing proposals to cut the number of MPs.

"The government is clear that the commission's primary task should be to examine how this house and parliament as a whole can deal most effectively with business that affects England wholly or primarily, when at the same time similar matters in some or all of Scotland, Wales and Northern Ireland are lawfully and democratically the responsibility of the separate parliament or assemblies," Harper said.

Many English backbenchers across all the major parties have been critical of and irritated by the issue. As she unveiled her bill in February, Baldwin said the West Lothian question came from the "heart of middle England".

She told the Commons: "How can it be right for it to be possible for potentially decisive pieces of legislation to be voted on in this place by, and carried by a majority of, members of parliament who are not legislating on behalf of their own constituents? That is not a question that we can carry on parking in that car park for ever."

Tom Harris, the Labour MP for Glasgow South, said he disagreed fundamentally with limiting MPs' voting rights. He said the Conservatives had relied heavily on Northern Irish unionist votes at Westminster for 50 years, even while Northern Ireland had its own legislature.

It was right to do so, he said. "We're a UK parliament. MPs always have responsibilities outside their own constituencies and even outside their nations. MPs vote on issues affecting Libya, for example, and I don't have many Libyans in my constituency."

He said the ability of Scottish or Welsh or Northern Irish MPs to control or influence English policy was overstated. There were far more English MPs than those from other nations or areas: there are currently 533 English constituencies against 59 in Scotland, 40 in Wales and 18 in Northern Ireland.

The UK government's legislation to cut the total number of MPs to 600 for the next general election in 2015 will leave England with between 500 and 502 seats, depending on the size of the electorate in 2015, Scotland with 50 to 52, Wales with 30 and Northern Ireland with 16.

"My bottom line is this: Scotland got devolution because it is a small nation, and it's easily possible for every single Scottish MP to vote one way and be out-voted by a small fraction of English MPs, but Scottish MPs don't decide English issues. You would need every single non-English MP to vote in that direction."

Eddie Bone, chairman of the Campaign for an English Parliament, said the issue needed urgently to be addressed as discontent in England about the "imbalance" between Westminster and the devolved areas was increasing rapidly, particularly with the upsurge in support for the Scottish National party.

"If they don't deal with it soon, they will have missed the window of opportunity with the people of England to save the union," Bone said.

Elfyn Llwyd MP, Plaid Cymru's constitution spokesman, said it was time for a federal system: "The problem is that Westminster is trying to do two jobs. It is trying to act as both an England and a UK parliament.

"England deserves to have its own administration to deal with issues which affect England only. This would then ensure that there is a clear distinction between what is a matter for England and what is a matter for other countries too. The lines are too blurred as they are."