Labour party members have stood by disgraced Keith Vaz, despite his resignation from a key Commons post over prostitution allegations, describing him as “an excellent MP”.

The veteran Labour MP's constituency party has shrugged off calls for him to stand down from Parliament over the scandal, saying: “Certainly not – that's his private life.”

Mr Vaz bowed to overwhelming pressure when he resigned as chairman of the influential Home Affairs Select Committee, after the allegations that he paid for sex with male prostitutes.

In a statement, issued a little more than an hour before a showdown meeting with other committee members, he said: “Those who hold others to account, must themselves be accountable.”He did not refer directly to the hugely damaging Sunday Mirror story that he paid for the services of two male escorts, told them to bring poppers and offered to pay for cocaine. But he wrote: “It is in the best interest of the Home Affairs Select Committee that its important work can be conducted without any distractions whatsoever.

“I am genuinely sorry that recent events make it impossible for this to happen if I remain chair. The integrity of the select committee system matters to me.”

Mr Vaz added: “This is my decision, and mine alone, and my first consideration has been the effect of recent events on my family.”

The Leicester East MP's position has been further weakened by fresh details which undermined his claim that he had been set up in a newspaper sting operation.

Some of his constituents have called for him to resign as an MP and Conservative Andrew Bridgen, who has demanded police and parliamentary investigations, said: “I have long been of the opinion that Keith Vaz is not fit to be an MP.”

On Monday, Theresa May hinted that she thought Mr Vaz should go, telling journalists: “I think overall what people look for is confidence in their politicians.”

But John Thomas, the chairman of the Leicester East constituency party, told The Independent: “We have every confidence in our MP. We have stood by him all the way, he is an excellent MP. We are only concerned about the job that he does for his constituents, which for all these years has been excellent. What he does with the Home Affairs Committee is something extra and not a concern for us.”

Mr Thomas condemned what he called a “tabloid sting”, adding: “They paid people to do that, didn’t they. It was bloody outrageous.”

Mr Vaz's downfall as a committee chairman marked the most serious setback in the career of Britain's most high-profile Asian MP – a magnet for controversy since entering Parliament in 1987. In those 29 years, he became embroiled in a series of financial allegations, sleaze investigations and conduct complaints, earning the nickname Mr Vaziline for his ability to survive.

At the same time, he built a stronghold in Leicester East, turning a thin majority of just 1,924 in 1987 into a massive one of 18,352 last year, even as Labour crashed to defeat nationally.

Conservative MP Tim Loughton has taken over temporary leadership of the Home Affairs Committee, before the election of a Labour successor – probably ex-leadership contender Chuka Umunna.