* Briton Usman Khan, 28, named as attacker who killed two
* Khan was convicted in 2012 for plot, released in 2018
* PM seeks tougher sentences as crime becomes UK election issue
* Opposition calls for full investigation, says questions raised
* IS says its fighter carried out attack, provides no evidence (Adds White House statement, paragraph 21)
By Costas Pitas and Guy Faulconbridge
LONDON, Nov 30 (Reuters) - The London Bridge attack pushed law and order towards the top of the British political agenda on Saturday, with days to go before a snap election, after police said the assailant had previously been convicted of terrorism offences but freed early from prison.
Usman Khan, wearing a fake suicide vest and wielding knives, went on the rampage at a conference on criminal rehabilitation beside London Bridge on Friday, killing two people. The 28-year old Briton was wrestled to the ground by bystanders then shot dead by police.
Police said on Saturday that Khan had been convicted in 2012 for his part in an al Qaeda-inspired plot to blow up the London Stock Exchange. He was released in December 2018 subject to conditions.
Jeremy Corbyn, leader of the main opposition Labour Party, criticised the government's sentencing policies.
"There's got to be a very full investigation," said Corbyn who is seeking to depose Prime Minister Boris Johnson in the election on Dec. 12 but trails in opinion polls.
"I think there is also a question about what the probation service were doing ... and whether the parole board should have been involved in deciding whether or not he should have been allowed to be released from prison in the first place," he said.
Earlier, Johnson said the attack was a terrorist act and vowed to end a practice whereby serious offenders can be automatically let out of prison early.
"I have long said that this system simply isn't working," he said after visiting the scene of the attack on Saturday.
Those convicted of a serious terrorism offence should face a mandatory minimum sentence of 14 years, he said later.
Islamic State said the attack was carried out by one of its fighters and was in response to its calls to target countries that had been part of a coalition fighting the jihadist group, according to its Amaq news agency. The group did not provide any evidence for its assertion.
A man and a woman were killed in the attack, with local media naming one of the victims as Jack Merritt, a course coordinator for Learning Together, a prisoners' rehabilitation programme which held the conference at Fishmongers' Hall.
Three people remain in hospital with two victims in a stable condition while a third person is suffering from less serious injuries, according to the National Health Service.
ECHOES OF 2017
Police said they were continuing their investigation by searching two addresses in the Staffordshire and Stoke areas of central England, with the country's top counter-terrorism officer saying they were not looking for any other suspects.
"We have found no evidence to suggest anybody else was involved in this attack," said Neil Basu. "Our investigative priority at this time is to ensure that there is no related outstanding threat to the public."
London Bridge was the scene of an attack during the 2017 election when three militants drove a van into pedestrians and then attacked people in the surrounding area, killing eight people and injuring at least 48.
Islamic State said its fighters were responsible for that attack, but the British authorities have cast doubt on those claims. The 2017 attack focused attention on cuts to policing since the ruling Conservatives took power in 2010.
Friday's attack prompted a pause in election campaigning, but scaled-back activities resumed on Saturday ahead of the election that could decide the fate of Brexit.
Five polls published late on Saturday showed the Conservatives ahead of Labour but with margins ranging from six to 15 points. Pollster BMG said it was possible no party wins a majority in the 650-seat parliament.
On Sunday, Corbyn will condemn foreign interventions such as the U.S.-led invasion of Iraq in 2003 for stoking hatred, The Observer newspaper reported as security and law and order feature more prominently in the campaign.
U.S. President Donald Trump, who is due to attend a NATO summit in London next week, spoke with Johnson on Saturday and expressed his condolences over the attack, the White House said in a statement.
Britain's police and politicians were joined on Saturday by Queen Elizabeth in praising those who intervened to thwart the assailant.
"I express my enduring thanks to the police and emergency services, as well as the brave individuals who put their own lives at risk to selflessly help and protect others," she said. (Additional reporting by William Schomberg in London, Hesham Abdul Khalek in Cairo, and Raphael Satter in Washington; Editing by Frances Kerry, Pravin Char, Marguerita Choy and Daniel Wallis)
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