Gordon Brown has revealed he ordered that Andrew Mountbatten-Windsor be questioned about incurring “unacceptable costs” as a trade envoy in 2008, as he called for the police to widen their inquiry to include the use of public funds.

The former prime minister said he asked a colleague from the business department to question Mountbatten-Windsor about his travel expenses.

In a piece for the New Statesman, Brown said the former prince regularly used RAF flights, and he was told his response was to ask whether the government seriously believed he should have to travel on commercial flights.

Mountbatten-Windsor was arrested in February on suspicion of misconduct in public office as police investigated his dealings with the convicted child sex offender Jeffrey Epstein. He has been released under investigation and has denied any wrongdoing.

Police had been assessing allegations that Mountbatten-Windsor shared sensitive information with Epstein when he was a UK trade envoy.

Brown, who was prime minister from 2008 to 2010, said the investigation into Mountbatten-Windsor should also consider his use of public funds.

“Police must now interview officials and ask for records from three government departments – the Ministry of Defence, the Department for Business and Trade and the Foreign Office – all involved in managing his trips while serving as UK trade envoy,” he wrote in the New Statesman.

“While serving as trade envoy, the former prince regularly used RAF flights. We must now question whether public funds were used in pursuit not just of his public duties but of his alleged private liaisons and even private business arrangements.”

Brown also said that when he was chancellor, the then prince demanded a fleet of aeroplanes separate from the RAF, provided by public funds. Brown said he turned down the request and informed the queen.

Brown wrote: “Emails in the Epstein files show the then prince claiming credit for having secured the privatisation of helicopters used by the royal family. Now, Andrew wanted the same arrangement for airplanes. The then prince’s proposal was that the government pay for the royal family franchising its own fleet of planes. The costs seemed prohibitive. I turned down his proposal and reported directly to the queen that the country could not afford such a plan.”

Brown called for authorities to re-interview Andrew not just over possible breaches of the Official Secrets Act but over his use of public funds and any links to allegations that Epstein trafficked women into the UK.

He highlighted reports drawing on the Epstein files about incidents in which women were allegedly brought to UK locations such as Sandringham and Buckingham Palace, who may have been trafficked into the country by Epstein.

The Guardian has previously reported that British police forces are considering whether flights linked to Epstein that arrived and took off from British airports merit a full criminal investigation, in case they were trafficking women into the UK for abuse.

The six forces considering claims about the Epstein flights into airports in their area are Bedfordshire, Essex, Norfolk, West Midlands, the Met and Police Scotland.

A spokesperson for the Metropolitan police told the New Statesman they were “aware of reporting regarding properties in London linked to Jeffrey Epstein and allegations that women living in them were victims of sexual abuse”. They said no complaints had been made to the force by any women involved.

Brown wrote: “The king has said that no one should be above the law, and alongside the police investigation, a select committee in parliament should examine how public funds were used, and whether a cover-up took place that prevented Andrew from being interviewed by US investigators.”

Mountbatten-Windsor has been approached for comment.