Victims “clearly want action” and the time has passed for a new national inquiry into grooming gangs, the woman who led a seven-year inquiry into child sexual abuse has said.

Prof Alexis Jay told BBC Radio 4’s Today programme that “people should get on with” implementing her recommendations and “locally people need to step up to the mark and do the things that have been recommended”.

“We’ve had enough of inquiries, consultations and discussions – especially for the victims and survivors who’ve had the courage to come forward,” she said.

The Conservatives and Reform UK have called for a national inquiry into grooming gangs after the subject came under the spotlight, in part due to interventions on social media from Elon Musk.

The Labour government has rejected calls for a new national inquiry, saying it will implement the recommendations of the Jay Review.

Prof Jay said the row over calls for a new inquiry was “distracting from the issues” and she was “very unhappy with the politicisation of child sexual exploitation” done in a “very uninformed way”.

However she added that the row may have given “some kind of impetus to move forward” after the home secretary announced a new offence to prosecute those who cover up or fail to report child sexual abuse.

Prof Jay declined to answer when asked whether she felt billionaire Musk knew what was going on in Oldham, where the council has been refused a public inquiry.

But she told BBC Radio 4’s Today programme: “I have heard very little in the last few days about the appalling and lifelong effects that child sexual abuse can have on people.

“I am pleased that the subject matter and the inquiry recommendations are finally getting the attention they deserve but this is definitely not the way I would have chosen for it to happen, but it has had the effect of moving on the agenda.”

On Monday, Home Secretary Yvette Cooper announced those who cover up or fail to report child sexual abuse could face professional or criminal sanctions under a new offence to be introduced this year.

The proposal was one of 20 recommendations made by Prof Jay following her seven-year inquiry into child sexual abuse, which concluded in 2022.

Cooper said the change would be added to the Crime and Policing Bill this spring.

Alex Davies-Jones, the government’s minister for victims and violence against women and girls, said a date had not been fixed for when all 20 recommendations of the Jay Review will be implemented.

She told BBC Breakfast: “We have been in government for six months – the previous government had years to implement these recommendations and sat on their hands instead of actually acting.”

Maggie Oliver, a former Greater Manchester police detective who resigned in 2012 over poor handling of abuse cases in Rochdale, told the BBC the home secretary’s statement on child abuse was “a bit of a kneejerk reaction to international horror at what has happened in our country”.

The Conservatives’ shadow justice secretary Robert Jenrick has called for a national inquiry and said “what we’ve learnt more recently is the sheer scale of what is happening”.

“The Jay Review, for example, looked at six towns. We now suspect at least 50 towns have had grooming gangs of this kind,” he told BBC Breakfast.

“It’s right we have a full national inquiry so we can get to the truth, we can ensure the victims have justice, that we can try to prevent other vulnerable young girls from being in this position again, and the frankly cowardly officials and councillors who have covered this up can also be brought to justice.”

Asked whether the Conservatives had done enough to tackle the issue in government, Jenrick said “more needs to be done”.

He said: “I have long advocated going further than that and saying you should have a full-life sentence if you are a grooming gang perpetrator, so you never see the light of day, so you go to jail, you don’t step foot out on the streets of our country in 10 years or so, as is happening at the moment.

“This is one of the most appalling racially aggravated crimes in our country’s history. It must be taken more seriously by everyone.”

Musk – the world’s richest man and an adviser to US President-elect Donald Trump – has faced criticism after he called safeguarding minister Jess Phillips a “rape genocide apologist”.

His remarks came after Phillips rejected a request for the government to lead a public inquiry into child sexual exploitation in Oldham.

She instead instructed Oldham Council in October to launch its own local inquiry into historic child sexual abuse in the town, similar to inquiries set up in Rochdale and Telford.

Musk has also accused Prime Minister Sir Keir Starmer of being “complicit in the rape of Britain” and suggested Sir Keir had failed to properly prosecute rape gangs while director of public prosecutions.

Speaking at a news conference on Monday, Sir Keir defended his record in his former role, saying when he left “we had the highest number of child sexual abuse cases being prosecuted on record”.

He said he enjoyed robust debate but it had to be “based on facts and truth, not on lies”.

The prime minister said the online debate around grooming gangs had now “crossed a line”, resulting in threats against MPs, including Phillips.