The BBC needs to “get a grip quicker” and complete reports and investigations sooner following controversies such as the broadcast of Bob Vylan at Glastonbury, the head of regulator Ofcom has said.

Dame Melanie Dawes said the corporation had “some own goals” over its handling of the punk-rap duo’s performance last month and a documentary about Gaza that was withdrawn in February.

At Glastonbury Bob Vylan led a chant of “death, death to the IDF [Israel Defence Forces]” and made other derogatory comments.

The BBC previously issued an apology to viewers, especially the Jewish community, and promised to take action to “ensure proper accountability”.

Reports into both broadcasts are expected to be published soon.

The review looking into the broadcast of Gaza: How to Survive a Warzone is due to be published next week, Dame Melanie said. The programme was pulled by the BBC after a link between its 13-year-old narrator and Hamas emerged.

Speaking on the BBC’s Sunday With Laura Kuenssberg programme, Dame Melanie said: “I think it’s very frustrating that the BBC has had some own goals in this area, with the Gaza documentary and then with the Glastonbury coverage, and it does start to erode public trust and confidence.

“I think I would say that, above all what frustrates me and others, is that when these things go wrong it can take a long time for the BBC to see that something’s happened when everybody else was there within a matter of hours.

“So I would say to the BBC I think they need to get a grip quicker, get these reports and investigations concluded sooner, otherwise there is a real risk of a sort of loss of confidence in the BBC, which is a shame.”

On the review into the Gaza documentary, a BBC spokesperson said findings will be published as soon as possible, adding: “It is vital that this work is done as quickly as possible, but it must also be thorough and follow a proper process.”

The BBC is also expected to answer a series of questions asked by Culture Secretary Lisa Nandy over the Bob Vylan performance.

In a letter to Director General Tim Davie, Nandy asked him to explain by 14 July the broadcast delays, staffing, decisions making, contingency plans and the next steps.

The BBC also said it will no longer broadcast live performances deemed “high risk” – as Bob Vylan had been assessed – and its director of music, Lorna Clarke, also reportedly stepped back from her day-to-day duties.

Asked on the programme whether Dame Melanie had faith in the BBC leadership, she replied: “I think it is a tough job at the top of the BBC.

“I think the [BBC] Board and senior team need to get a bit quicker at recognising when something has gone wrong and get a grip of the actions that they need to take or there is going to be a real risk that the BBC loses confidence in what it delivers for the public.

“We are going to have to see over the next week, I think we are expecting the Gaza report early in the coming week. We have asked a lot of questions about the Glastonbury coverage, the BBC has got a lot on its plate that it needs to address.

“I think it is important to also recognise that they do deliver a very high-quality job for the public usually, but it is these own goals that are very frustrating they need to be quicker to get on to, quicker to grip and quicker to put right.”

Transport Secretary Heidi Alexander told the programme the BBC needed “to do a rapid investigation of what has happened in relation to the Glastonbury incident”.

She said: “They need to do it thoroughly because at the end of the day the BBC needs to maintain the trust of its audience.”

Shadow home secretary Chris Philp said Bob Vylan was “inciting violence and hatred” and suggested the BBC should be prosecuted for broadcasting the footage.

“There should be an investigation and if, in the police’s opinion, the Crown Prosecution Service’s opinion, there is a reasonable prospect of conviction then it should be taken to court.

“That’s the right process and they should go through that, for sure. There’s no exemption just because it’s the BBC.”