Opposition parties have described the arrangement as "shocking" and called for an urgent investigation into possible conflicts of interest.

Liz Truss appointed Mr Fullbrook as her chief of staff earlier this month.

His salary is reported to be paid via his own lobbying firm Fullbrook Strategies, which was set up in March.

This is despite the fact that the firm's website saying it "has currently suspended its commercial activities".

A spokesperson for Mr Fullbrook told BBC News: "This is not an unusual arrangement. It was not put in place for tax purposes and Mr Fullbrook derives no tax benefit from it."

However, the spokesperson did not respond to questions about whether Fullbrook Strategies had suspended "commercial activities" and, if it had, why it might be hiring Mr Fullbrook on secondment to the government.

Downing Street and the Cabinet Office, which is directly responsible for employing Mr Fullbrook, have both refused to confirm exactly how he is employed and paid.

However, a Cabinet Office spokesperson said: "It is not unusual for a special adviser or civil servant to join government on secondment.

"The government will pay the salary of an employee on secondment, including costs such as Employers National Insurance contributions to the seconding company.

"This has been cleared by the Propriety and Ethics team in Cabinet Office."

But the Institute for Government think tank told BBC News that this did appear to be an unusual arrangement.

Catherine Haddon, senior fellow at the institute, and a former employee in Downing Street, said she could not think of another situation where a special advisor would be on secondment rather than being employed directly by the civil service.

Ms Haddon said there would be a particular concern about any potential conflicts of interest that might arise. She pointed to recent concerns about MPs' second jobs and said the government would need to be "upfront about what they are doing to manage any conflicts of interest".

Liberal Democrat deputy leader Daisy Cooper said: "Liz Truss's administration is proving to be nothing more than the same as Boris Johnson's".

She added: "We need to see an urgent independent investigation into any conflicts of interest."

Labour's deputy leader Angela Rayner said: "The shocking revelation that the prime minister's chief of staff is on loan from a lobbying company, not actually employed by the government, raises serious questions about the new prime minister's judgement."

Ms Rayner said a Labour government "would create an Independent Ethics and Integrity Commission to clean up public life and restore the basic standards we expect".