The BBC director general, Tony Hall, and South Yorkshire police are facing a parliamentary inquiry over the leaking of highly sensitive information about the investigation of Sir Cliff Richard as an independent inquiry into the affair was announced.

Hall and David Crompton, the South Yorkshire chief constable, were told on Monday to be ready to give evidence to MPs over the force’s handling of the inquiry into historical child abuse allegations.

Keith Vaz, the Commons home affairs committee chairman, wrote to the pair demanding answers, adding that he was “concerned by the methods or process” followed by the corporation over its live coverage of the police search.

The BBC has been accused of leading a witch-hunt against the 72-year-old singer after it was apparently tipped off about the timing of the police raid on Richard’s £3.5m Berkshire residence last Thursday. Richard, who remains on holiday in Portugal, has vehemently denied any wrongdoing over an allegation of sexual abuse on a boy under 16 at a Christian rally in Sheffield in 1985.

In a letter seen by the Guardian, Vaz pressed Hall to explain how the broadcaster first learned about the planned police search and who authorised a news helicopter to beam the raid live on television. Vaz said in the letter: “We understand and support the right of the media to report matters in the public interest but are concerned by the methods or process that may be followed to garner this information.”

As the fallout from the search continued on Monday, Shaun Wright, South Yorkshire’s police and crime commissioner, summoned Crompton to an urgent meeting to explain the events leading up to the search. It is understood that the meeting is not a formal interview but is a key part of the inquiry into the events that led to the police search of Richard’s residence.

A BBC spokesperson said: “We have received the letter and will respond in due course. Mr Vaz understands and supports the right of the media to report matters in the public interest. The BBC’s editorial independence is protected by our royal charter and is highly valued by the public. The BBC does not name its sources, nor is it appropriate to go into detail around editorial processes.”

Wright also said that Andy Trotter, former chief constable of the British Transport police and former chair of the national police communications advisory group, would lead an independent investigation to determine whether South Yorkshire police’s actions complied with media guidelines issued by the College of Police Guidance.

BBC insiders revealed that its coverage of the raid was approved by the deputy news director, Fran Unsworth, and came amid increased pressure in its news operation to beat rivals to exclusive stories. James Harding, the former Times editor who is the BBC’s director of news and current affairs, was on holiday last week.

Unsworth and members of the BBC’s legal department contacted news teams to give the reporters the all-clear 10 minutes before its coverage was aired. The reports prompted criticism from politicians and public figures, including former BBC broadcaster Michael Parkinson, and its legality was questioned by the human rights lawyer Geoffrey Robertson.

Harding wants BBC News to be breaking more stories, setting the pace and “driving the daily agenda”. There was praise for the BBC reporter Dan Johnson, who got the scoop, but also reservations among some that the live helicopter footage had been over the top. A BBC spokeswoman said: “A BBC journalist approached South Yorkshire police with information about the investigation.

“We followed normal journalistic practice and agreed not to publish a story that might jeopardise a police inquiry. We have also confirmed that South Yorkshire police were not the original source for the story.”