The Conservative MP Geoffrey Cox has agreed to an additional two weeks of work representing ministers from the British Virgin Islands this month while parliament is sitting, it has emerged.

The former attorney general has come under intense scrutiny in recent days over his second job as a barrister, which has earned him almost £6m on top of his MP’s salary.

With the Conservative party facing a slew of sleaze allegations, government ministers have pointedly refused to defend Cox against allegations that he put lucrative outside work before his constituents – something he has denied.

While Cox will not travel to the Caribbean, and will only have to appear once before the inquiry panel looking into the country’s governance standards, he is scheduled to work on the complex inquiry from 15 to 26 November, official records show.

The commitments prompted renewed criticism of Cox’s focus on his parliamentary duties.

He is representing a series of British Virgin Islands (BVI) government figures, including the prime minister, Andrew Fahie, during a formal commission of inquiry examining claims of misgovernance and abuse of office.

He travelled to the country at various points since April this year, and used procedures in place amid Covid restrictions to cast proxy votes in his absence. Cox has also appeared virtually from his parliamentary office, prompting Labour to seek an investigation into whether this broke Commons rules against using such facilities for private work.

In the most recent meeting of the inquiry commission, on 22 October, the inquiry head, Sir Gary Hickinbottom, a retired British judge, set out times for future hearings, including those sought by the BVI attorney general, Dawn Smith, among those represented by Cox.

Smith had notified the commission “of dates of availability for counsel of her choice – I think that is Sir Geoffrey – for the period the 15 to 26 November”, Hickinbottom said, according to an official transcript of the hearing.

After Hickinbottom had set out this and various other logistical matters, Cox, who was appearing remotely from an unknown location, with the background blurred, replied: “I think our initial reaction is that most of those directions seem perfectly achievable.”

A spokesperson for Cox said this schedule did not mean Cox would appear before the commission throughout this period, when the Commons will be sitting.

“Sir Geoffrey is assisted by a legal team who will carry out most of the work,” they said. “Therefore, he will only need to make himself available for a period of approximately two hours on one day, during that time. This will not conflict with his parliamentary responsibilities.”

But asked what other duties Cox would have over the fortnight connected to the BVI inquiry aside from appearing before the commission panel, the spokesperson did not respond.

Wendy Chamberlain, the Liberal Democrat chief whip, said: “Geoffrey Cox clearly sees being an MP as his second job. He absolutely no time or inclination to actually do the work his constituents sent him to Westminster to do.”

The Labour MP Andrew Gwynne said: “MPs should be in parliament representing their constituents. Boris Johnson’s refusal to act proves he’s lost control, doesn’t care, or both.”

Cox also makes money by renting out a three-bedroom flat overlooking Battersea Park in south London, one he and his wife bought in 2004 for £535,000. It is thought to be rented out for between £3,000 and £4,000 a month, a figure based on a comparison with similar rental properties in the area.

The tenants said they have had no direct contact with Cox, their landlord, and had simply rented the flat via an agency. Asking not to be named on Thursday, they said they had only moved in a few months earlier.

Despite owning a London property, which he has owned for more than a decade, records from the Independent Parliamentary Standards Authority, which pays MPs expenses, show that Cox had moved in November 2017, and started claiming £1,900 a month in rent for a separate residential property.

The purchase cost of the original flat was initially part-funded by taxpayer payments of £1,750 a month towards mortgage interest costs, after Cox was elected in 2005. This was under the old system of funding MPs although that was scrapped after the expenses scandal towards the end of the decade.

In August, Fahie refused to say how much his government was paying the law firm Withers for its overall legal representation, but said more than $3m (£2.25m) had been spent so far.

At one hearing, on 21 June, Cox stressed that the minister he was representing “accept entirely that it is central to the democratic idea that the purpose of elected office is to serve the public – it is not to enrich the office holder”.