The Commons will vote on Wednesday on whether to establish a parliamentary inquiry into David Cameron’s lobbying activities.

A plan put forward by Labour would create a new Commons select committee to investigate lobbying, including the former prime minister’s activities in support of collapsed lender Greensill Capital.

If MPs approve the motion, the cross-party committee would investigate whether current laws are sufficient to prevent “inappropriate lobbying” of ministers and officials.

Shadow chancellor of the Duchy of Lancaster Rachel Reeves urged Tory MPs to back the motion if they want to “stop the cronyism rampant in their party and in government”.

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Labour’s Rachel Reeves claimed /cronyism’ is ‘rampant’ within the Tory party (Jonathan Brady/PA)

Opposition day motions are not usually binding on the Government, but because this is calling for Parliament rather than ministers to establish an inquiry it would lead to the creation of the Investigation Into Lobbying Of Government committee.

The proposed committee would have the power to “send for persons, papers and records” – giving it the ability to summon Mr Cameron and ministers including Chancellor Rishi Sunak and Health Secretary Matt Hancock to answer questions in public.

Mr Cameron sent text messages to the Chancellor and reportedly took Mr Hancock for a “private drink” with his employer Lex Greensill as part of his lobbying activities.

Labour has claimed that a separate inquiry established by Boris Johnson, which will be led by lawyer Nigel Boardman, will be a “Conservative cover up”.

Ms Reeves said: “Any Conservative who wants to stop the cronyism rampant in their party and in Government must vote with Labour this week to uncover once and for all the truth behind this scandal.

“The Greensill scandal is just the tip of the iceberg in Conservative cronyism, which has been endemic during the pandemic and long before – laced through billions of pounds of contracts paid for by taxpayers and a slew of troubling senior appointments.

“The Conservatives cannot be trusted to mark their own homework on this.

“The Boardman investigation has all the hallmarks of a Conservative cover up – the British public, especially those with their jobs on the line as a result of Greensill’s collapse, deserve answers.”

The motion will not pass without the support of Conservative MPs, something that is unlikely on an opposition proposal.

But the move maintains pressure on ministers over the affair and highlights the issues raised by Mr Cameron’s lobbying activities as he sought to win access to an emergency coronavirus loan scheme for his employer, Lex Greensill.

The former prime minister, who sent text messages to the Chancellor and contacted other ministers, has admitted that he should have communicated with the Government “through only the most formal of channels”.

Mr Cameron also reportedly took Mr Hancock for a private drink with Mr Greensill to discuss a payment scheme later rolled out in the NHS.

Greensill Capital, which collapsed into administration in March, was the biggest backer for Liberty Steel, a firm which employs thousands of workers around the UK and now faces an uncertain future.