As Tory backbench anger over human rights rulings grows, PM says commission looking into possibility of creating British bill of rights will be established soon

A coalition commission into the possibility of setting up a British bill of rights will be established shortly, David Cameron has announced.

The coalition agreement set out plans for the review into a British bill of rights, and there has been growing pressure from Tory backbenchers to press ahead with the commission in the wake of Conservative anger over the impact of human rights rulings.

That anger has been fuelled by the need to comply with the European court ruling that the UK must give some prisoners the right to vote.

A further ruling by the UK supreme court that sex offenders must be given the right to challenge their place on the sex offenders register only added to Tory anger.

Conservative sources appeared to admit that likely disagreements between themselves and the Liberal Democrats on the issue of a UK bill mean the Tories would have to undertake separate policy work to put the issue into a 2015 election manifesto.

Lord McNally, the justice minister and a senior Liberal Democrat, has said he would resign from the government rather than see the UK withdraw from the European convention, to which Britain has been a signatory for more than 60 years.

In recent days, the rightwing Policy Exchange thinktank said it was possible to reform the relationship between British law and the European convention.

The attorney general, Dominic Grieve, also pointed out that there was no requirement for Britain to remain a signatory to the European convention, saying parliament had the last word on the issue and adding that some members of the UK judiciary favoured withdrawal.

Grieve believes the European court of human rights – which is separate to the EU court of justice – has become too intrusive.

The Cabinet Office minister, Francis Maude, said there was growing disquiet at some judicial rulings that flew in the face of common sense.

It has been argued by some that Britain could have its own bill of rights but remain signatories to the European convention.

In a lengthy speech as the shadow home secretary, Grieve argued that the current Human Rights Act had been "interpreted as requiring a degree of deference to Strasbourg that I believe was and should be neither required nor intended".

Instead, he said, a new bill of rights, which would replace the Human Rights Act, would make it clear that British courts could allow for UK common law to take precedence over decisions by the European court of human rights in Strasbourg.

Grieve promised: "We would want to reword it to emphasise the leeway of our national courts to have regard to our own national jurisprudence and traditions and to other common law precedents while still acknowledging the relevance of Strasbourg court decisions.

"My own inclination would be to use the convention rights, as currently drafted, as a starting point. To do otherwise appears to me to risk pointless confusion."

In contrast, writing in the Guardian last year, McNally argued: "The European convention on human rights is part of our DNA. It is not 'someone else's law'. It was never imposed on Britain. The UK proposed the creation of the convention at the end of the second world war."

But he said he was happy to look "afresh at the way rights are protected in the UK, to see if things can be done better and in a way that properly reflects our legal traditions".