Police have searched the Bradford home of Paul Flowers, the gay former Co-op bank chairman who continues to face intense public scrutiny about his private life.

Mr Flowers, a Methodist minister, is under investigation by police after being filmed allegedly buying and using illegal drugs including crystal meth, crack cocaine and ketamine.

A spokesman for West Yorkshire Police said: “Officers executed a search warrant at an address in Hollingwood Lane, Great Horton, [Bradford] yesterday as part of an investigation into alleged drugs offences arising from a national Sunday newspaper story.”

Mr Flowers was the chairman of the Co-op Bank from 2010 until May this year when he stepped down as the bank hurtled to near financial collapse.

Today, David Cameron told the House of Commons there were “a lot of questions that have to be answered” about Mr Flowers’ time at the head of the bank for three years.

Mr Cameron said: “The Chancellor will be discussing with the regulators what is the appropriate form of inquiry to get to the bottom of what went wrong here.

“But there are clearly a lot of questions that have to be answered. Why was Rev Flowers judged suitable to be chairman of a bank? Why weren’t alarm bells ringing earlier, particularly by those who knew?

“I think it will be important in the coming days that if anyone does have information they stand up and provide it to the authorities.”

He added: “The first priority is to safeguard this bank and to make sure that it is safeguarded without using taxpayers’ money.”

Yesterday, Tory Chairman Grant Shapps wrote to Labour leader Ed Miliband, after it was revealed Mr Flowers had resigned as a Labour councillor in Bradford in 2011 after “inappropriate but not illegal adult content” was found on a computer he used.

In the letter, Mr Shapps wrote: “Was your Shadow Chancellor, Ed Balls, aware of this when he accepted £50,000 to fund his personal office?

“When you met Mr Flowers on 6 March, 2013, did you discuss the £1.2 million loan agreement that the Labour Party entered into with the Co-operative bank, just weeks later?”

Mr Shapps also challenged Mr Miliband to give details of his private meetings with the minister and explain what advice the former Co-op chairman gave as a member of Labour’s business advisory group.

A spokesman for Mr Balls said: “The Co-op Group, not the bank, donated £50,000 to the shadow chancellor’s office, which was declared in the normal way at the time.

“Ed (Balls) has never discussed the donation with Paul Flowers. Ed’s been to a few events which Rev Flowers has also been at, but he’s never had a meeting or phone conversation with him.”

On Tuesday, Co-op Group chairman Len Wardle resigned, citing “serious questions” raised by the scandal surrounding Mr Flowers.

Later on Tuesday, Terrence Higgins Trust announced Mr Flowers would no longer be on the board of trustees for the charity.