The man who lost out on becoming one of the most powerful figures in British policing by the toss of a coin was among four men arrested during an investigation into a suspected £1m charity fraud.

Will Riches, 40, who quit as vice-chairman of the Police Federation of England and Wales earlier this week, was being questioned after detectives were called in to scrutinise its books in the latest turbulent episode for the organisation.

The inquiry – Operation Rutland – focused on a money transfer of about £1m to a charitable account in August 2015. The Charity Commission has been informed about the inquiry.

The case is being investigated by police in Surrey, the home of the organisation’s state-of-the-art £26m headquarters, and they arrested two men in their 50s and two in their 40s. Three of them are serving officers on secondment from their forces.

“We are carrying out a detailed and thorough investigation into allegations of fraudulent activity involving significant amounts of money,” said Detective Superintendent Karen Mizzi, who is leading the inquiry.

“Our enquiries are at an early stage but specialist officers, including our Economic Crime Unit, are investigating to establish whether any offences have occurred.”

The four men were arrested for alleged fraud through abuse of their positions and conspiracy to defraud.

The organisation, which represents 122,000 officers from constable to chief inspector, sits on vast reserves of tens of millions pounds but has been criticised for its opaque financial structure.

Following a raft of controversies that included the controversial role of regional officials in the Plebgate saga and accusations of lavish spending, the Home Secretary announced in 2014 that state funding for the organisation would end.

In a statement, the Police Federation of England and Wales said it was cooperating with the inquiry and said that day-to-day running of the organisation was unaffected. “Until the enquiry is complete, it would be inappropriate to comment further,” it said.