By Sachin Ravikumar and Elizabeth Piper

LONDON (Reuters) - UK Prime Minister Keir Starmer vowed on Tuesday to "leave no stone unturned" to uncover failings in preventing the killings of three girls at a Taylor Swift-themed event, saying an inquiry could lead to a change in terrorism laws.

Starmer defended his government's stance to not divulge many details earlier about the British teenager guilty of the killings by saying he did not want to collapse the case, but admitted there were failings.

Axel Rudakubana, 18, unexpectedly pleaded guilty on Monday to murdering Bebe King, 6, Elsie Dot Stancombe, 7, and Alice Dasilva Aguiar, 9, in the English town of Southport in July, and to producing ricin and possessing an al Qaeda training manual.

Shortly afterwards, the government said Rudakubana had been referred to Prevent, a counter-radicalisation scheme, three times, but no action had been taken. Police said no one ideology had been uncovered and the case was not treated as terrorism.

On Monday, the government announced a public inquiry into the murders, which led to riots around the country after false reports on social media said the suspect was a radical Islamist migrant. Opponents have accused Starmer and the police of covering up what they knew.

The prime minister said failures would be made public and the attack could show that Britain faces a new type of terrorism threat waged by "loners, misfits, young men in their bedrooms" committing extreme violence.

'NO STONE UNTURNED'

"I want to be crystal clear in front of the British people today. We will leave no stone unturned ... Nothing will be off the table in this inquiry. It will lead to change," Starmer told a press conference.

The main opposition Conservative Party, which made changes to Prevent after conducting a review while in power, welcomed the inquiry but said "there are many questions that remain unanswered", adding those who failed should be named.

The leader of right-wing Reform UK party, Brexit campaigner Nigel Farage, has branded handling of the case "the most appalling cover-up I think I've ever seen".

At the swiftly arranged press conference, Starmer was keen to get ahead of any new criticism.

In promising he would call out state institutions that had failed to prevent the killings, he hoped to lift the pressure on his government, which has struggled since winning power in July.

Starmer also faced criticism when he was England's chief prosecutor over his handling of a child sexual abuse scandal.

He said at the time, he had brought the men of mainly Pakistani heritage to justice and vowed, as prime minister, to act quickly after Southport.

"The senseless, barbaric murders of three young girls killed in Southport is a devastating moment in our history," he said. "Southport will be a line in the sand."

(Reporting by Sachin Ravikumar and Elizabeth Piper, additional reporting by Sarah Young, Andrew MacAskill, editing by Sharon Singleton)