Former Conservative cabinet ministers Matt Hancock and Kwasi Kwarteng told a fake overseas company looking for MP advisers that their daily rate for consultancy would be £10,000.

In a sting operation set up by campaign group Led By Donkeys, Mr Hancock and Mr Kwarteng both set out five-figure sums for what they would expect to be paid to advise a non-existent firm in South Korea.

There is no accusation of wrongdoing, with MPs permitted to seek employment outside of parliament.

When asked whether he had a daily rate during an online “interview”, Mr Hancock said: “I do, yes. It is 10,000 sterling.”

The Conservative former health secretary, who was stripped of the party whip by Prime Minister Rishi Sunak after he was announced as a contestant in last year’s series of ITV reality programme I’m A Celebrity… Get Me Out Of Here!, later said he had an hourly rate of “around £1,500”.

A spokesman for Mr Hancock said the West Suffolk MP had “acted entirely properly and within the rules”.

Former Tory chancellor Mr Kwarteng, when asked the same question, said: “I would say as an MP, obviously I don’t need to earn a king’s ransom.

“But I wouldn’t do anything less than for about 10,000 dollars a month.”

Mr Kwarteng, whose mini budget in September sent the value of the pound tumbling and mortgage rates soaring, went on to clarify that he would prefer the rate to be in pound sterling.

Told by a fake employee of the company they were considering offering between £8,000 and £12,000 per day, with the intention for him to attend six board meetings a year, Mr Kwarteng said: “OK yes, we’re not a million miles off. We can work with the numbers.”

Labour accused Tory MPs of using “their taxpayer-funded offices to line their own pockets”, calling the behaviour “shameful”.

Led By Donkeys, an anti-Brexit group, said it created a sham company called Hanseong Consulting, setting up a website and paying for a so-called “fake virtual office” in the South Korean capital Seoul.

It said, after consulting the register of MPs’ interests, it approached 20 MPs from different parties asking if they would join the phoney firm’s international advisory board.

The group sold the “company” as one with aims to expand into the UK and Europe, asking any would-be advisers to attend pretend board meetings held in a mix of locations, including allegedly in South Korea.

According to its preview video posted on social media, Led By Donkeys said 16 of the MPs approached were Tory, two Labour, one a Liberal Democrat and the other an independent.

Out of those contacted, five are said to have progressed to an online interview stage, including Mr Hancock and four Tories: Mr Kwarteng, former education secretary Sir Gavin Williamson, former minister Stephen Hammond and Sir Graham Brady, chairman of the 1922 Committee, an influential backbench body.

Sir Graham, according to the video, said he was “thinking something like £60,000 as an annual rate” for assisting the firm.

In a statement sent to Sky News, the senior Tory said he made clear to those behind the hoax that any work would have to fall “within the terms of the Code of Conduct”.

Mr Hammond is seen in the video published on Saturday, but no details of what was said have been aired as yet.

Led By Donkeys said Sir Gavin had turned down the opportunity to take discussions any further.

MPs are permitted to have second jobs on top of their role representing constituents.

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But external employment opportunities for those in Westminster have come under the spotlight in recent years, following former Tory cabinet minister Owen Paterson’s suspension from the Commons for breaching lobbying rules in 2021.

He later quit parliament following a furore after Boris Johnson’s administration attempted to rip up the standards body that dished out the punishment.

A spokesperson for Mr Hancock said in response to the sting operation: “The accusation appears to be that Matt acted entirely properly and within the rules, which had just been unanimously adopted by parliament.

“It’s completely untrue to suggest any wrongdoing and therefore absurd to bring Mr Hancock into this story through the illegal publication of a private conversation.

“All the video shows is Matt acting completely properly.”

Sir Graham said: “Having decided to leave the Commons at the next election, I have received a number of approaches regarding future opportunities.

“I did have an exploratory discussion with someone purporting to be recruiting an international advisory board for a South Korean investment house.

“I made it clear that any arrangement would have to be completely transparent and that whilst a Member of Parliament, I would only act within the terms of the Code of Conduct.

“I also made it clear that whilst I could be flexible in attending international meetings in person, this would be subject to some important votes or commitments in Westminster.”