Former Cabinet minister Sir Geoffrey Cox could face an investigation by the Commons standards tsar over claims he “broke the rules” by using his parliamentary office for his second job offering legal advice.

The Times reported that the former attorney general, who has faced criticism over his outside earnings, used his Westminster office to participate remotely to advise the British Virgin Islands in a corruption probe launched by the Foreign Office.

Conservative MP and QC Sir Geoffrey has earned hundreds of thousands of pounds for his work with the islands, while allegations have surfaced that he was based in the Caribbean earlier this year while using lockdown proxy voting rules to continue to have his say in the Commons.

Deputy Labour leader Angela Rayner said the alleged use of the office appeared to be “an egregious, brazen breach of the rules” and has written to standards commissioner Kathryn Stone asking her for “guidance on beginning a formal investigation on this matter”.

Ms Rayner said in her letter that the MP’s code of conduct was “very clear” that elected representatives ensure that “any facilities and services provided from the public purse is… always in support of their parliamentary duties” and “should not confer any… financial benefit on themselves”.

She added: “The member has clearly broken this rule based on the media reports we have seen.

“Members must be clear that they cannot use the estate for private financial gain and where there is such a stark conflict with public interest, they must face substantial consequences.”

The most recent register of financial interests showed that Torridge and West Devon MP Sir Geoffrey will earn more than £800,000 from Withers, an international law firm appointed by the British Virgin Islands (BVI) government in January.

Sir Geoffrey also disclosed in the register that from September 28 this year until further notice, he will be paid £400,000 a year by Withers for up to 41 hours of work per month.

In the British Virgin Islands commission of inquiry hearing on September 14, Sir Geoffrey can be heard in the online recording telling the commissioner: “Forgive my absence during some of the morning – I’m afraid the bell went off.”

The bell referred to could be the division bell that sounds off across the parliament estate to alert MPs to a vote taking place.

Earlier in the proceedings, Sir Geoffrey appears to vacate his seat for about 20 minutes at around the two-hour mark in the video footage.

His Commons voting record shows that he voted in person on six occasions on September 14 to push through the Government’s health and social care levy.

Ms Rayner said: “This appears to be an egregious, brazen breach of the rules.

“A Conservative MP using a taxpayer funded office in Parliament to work for a tax haven facing allegations of corruption is a slap in the face and an insult to British taxpayers.

“The Parliamentary Commissioner for Standards must investigate this, and the Prime Minister needs to explain why he has an MP in his parliamentary party that treats Parliament like a co-working space allowing him to get on with all of his other jobs instead of representing his constituents.

“You can be an MP serving your constituents or a barrister working for a tax haven – you can’t be both and Boris Johnson needs to make his mind up as to which one Geoffrey Cox will be.”

The Liberal Democrats also waded in, with the party’s chief whip Wendy Chamberlain urging the QC to “save everyone the time and trouble of an investigation” and “come clean now”.

Ms Chamberlain added: “The real slap in the face is that this took place on the very same day he voted through a tax hike on millions of hardworking British people.”

The row over second jobs comes in the wake of a recommendation that former environment secretary Owen Paterson’s should be suspended for six weeks after the Commons Standards Committee found he had broken the centuries-old ban on paid lobbying by MPs.

In the bitter aftermath of the row, Mr Paterson announced he was quitting as MP for North Shropshire after 24 years, as an attempt by the Government to delay his punishment by ripping up the current standards system failed when opposition parties refused to offer their support.

Boris Johnson, who was previously well paid as a backbencher, including for his regular Daily Telegraph column, signalled that those in the Commons should focus on their electorates.

A spokesman for the Prime Minister, while refusing to be drawn on individual cases, said Mr Johnson thought an “MP’s primary job is and must be to serve their constituents and to represent their interests in Parliament”.

The No 10 spokesman said: “They should be visible in their constituencies and available to help constituents with their constituency matters.

“If they’re not doing that, they’re not doing their job and will rightly be judged on that by their constituents.”

The PA news agency has contacted Sir Geoffrey’s office for comment.