LONDON (AFP) - Prime Minister David Cameron admitted Wednesday that Britain had not done enough to counter domestic Islamic extremism and vowed to do more, after it emerged that a Swedish suicide bomber studied here.

"I think if we're frank on both sides of the House (of Commons), we have not done enough to deal with the promotion of extremist Islamism in our own country," he told lawmakers, referring to all political parties.

News that a suicide bomber who attacked a busy shopping street in Stockholm on Saturday had studied and lived in Britain has raised fresh soul-searching here about how to combat radicalism, five years after four home-grown bombers attacked the London transport system in 2005, killing 52 people.

"Whether it's making sure that imams coming over to this country can speak English properly, whether it's making sure we deradicalise our universities, I think we do have to take a range of further steps and I'm going to be working hard to make sure that we do this," Cameron said.

"Yes, we have got to have the policing in place, yes we've got to make sure we invest in our intelligence services, yes we've got to cooperate with other countries.

"But we've also got to ask why it is that so many young men in our own country get radicalised in this completely unacceptable way."

The man responsible for Sweden's first-ever suicide bombing is believed to have been Taimour Abdulwahab, who until recently had been living in Luton, north of London.

He was carrying a cocktail of explosives but succeeded in killing only himself.