* May back on campaign trail after London killings
* Police make new raids after 7 killed, 48 injured
* May under pressure over cuts to police numbers
* Labour's Corbyn backs calls for her to resign
* Polls show May's lead narrowing before Thursday election (Adds Trump, new barriers on bridges, background on Corbyn)
LONDON, June 5 (Reuters) - Britain's election campaign resumed in earnest on Monday with Prime Minister Theresa May's opinion poll lead narrowing and the focus firmly on her security record after an attack by marauding jihadis killed seven people in the heart of London.
In Britain's third Islamist attack in as many months, three men rammed a van into pedestrians on London Bridge on Saturday night before running into the bustling Borough Market area, where they slit throats and stabbed people indiscriminately.
All three attackers were shot dead by police, who made at least a dozen arrests in east London on Sunday and carried out further raids on Monday morning.
The attackers' identities are known but have not been disclosed.
"This was an attack on London and the United Kingdom, but it was also an attack on the free world," May said.
A Canadian and a French national were among those who died, while the 48 injured included people of many nationalities. Eighteen people remained in a critical condition.
Britain has received messages of solidarity from numerous world leaders including Donald Trump, although the U.S. president also struck a discordant note by issuing tweets criticising London Mayor Sadiq Khan.
Trump accused Khan of making a "pathetic excuse" for saying on Sunday morning that Londoners should not be alarmed. A spokesman for Khan had noted in response to an earlier Trump tweet that Khan's comment referred to the increased police presence on London's streets. May said Khan was doing a good job and it was wrong to say anything else.
A parliamentary election takes place on Thursday and May's spokeswoman said the government was working closely with police on security for the vote.
Saturday's rampage took place less than two weeks after a suicide bomber killed 22 children and adults at a concert in Manchester. In March, five people died after a man drove a van into pedestrians on London's Westminster Bridge and stabbed a policeman.
New security barriers were in place on Monday morning on several bridges in central London, including Westminster Bridge.
With the London attack dominating attention, a reduction in the number of police officers in England and Wales by almost 20,000 during May's six years as interior minister from 2010 to 2016 shot to the top of the election agenda.
"It's just a fact that, over the last seven years, we as a city have lost 600 million pounds from our budgets. We have had to close police stations, sell police buildings, and we've lost thousands of police staff," said London Mayor Khan, who is from the opposition Labour Party.
May did not answer repeated questions from reporters on the cutbacks but said counter-terrorism budgets had been protected and police had the powers they needed.
Her main opponent, Labour leader Jeremy Corbyn, backed calls for her resignation over the police cuts.
He said many people were "very worried that she was at the Home Office for all this time, presided over these cuts in police numbers, and now is saying that we have a problem".
May hit back by criticising Corbyn, a pacifist who has opposed some security legislation in parliament and expressed reservations in the past about police responding to armed attackers with "shoot-to-kill" tactics.
He sought to end that earlier controversy on Sunday by stating that he backed the full authority for the police to use whatever force is necessary to protect and save life as they did (at Borough Market), as they did in Westminster in March.
Corbyn's critics have often accused him of weakness on terrorism, citing his sympathy for members of the Palestinian group Hamas, Lebanon's Hezbollah and Sinn Fein, the former political wing of the Irish Republican Army. The IRA ran a 30-year armed campaign against British rule in Northern Ireland.
May's Conservative Party's lead over Labour has narrowed markedly from 20 points or more when she called the election in April to a range between one and 12 points now, although the Conservatives are still widely expected to win a majority.
The pound rose on currency markets, which favour May over Corbyn, after the latest ICM poll, taken between June 2 and June 4 and published on Monday, suggested the Conservatives were ahead by 11 points.
"TELL THEM CHRISSY SENT YOU"
Christine Archibald, a 30-year-old Canadian who had worked in a shelter for the homeless before moving to Europe to be with her fiance, was the first of those who died to be named.
"Please honour her by making your community a better place. Volunteer your time and labour or donate to a homeless shelter," her family said in a statement. "Tell them Chrissy sent you."
A vigil to honour the victims was due to take place at 6 p.m. (1700 GMT) at Potters Fields Park near London City Hall, which stands by the River Thames, a short walk from London Bridge.
The Islamic State militant group, which is losing territory in Syria and Iraq to an offensive backed by a U.S.-led coalition, claimed responsibility for the London Bridge attack, though it is unclear whether the attackers had links to the group.
London police chief Cressida Dick said that, while some of the recent attacks in Britain had international dimensions, they had a largely domestic "centre of gravity". Both the Westminster and Manchester attackers were British-born.
Khan, the first Muslim to be elected mayor of a major Western European city, was among those who denounced the ideology behind the recent attacks.
"I am angry and furious that these three men are seeking to justify their actions by using the faith that I belong to," Khan said. "I condemn this terrorist act but also the poisonous ideology these men and others follow." (Additional reporting by William Schomberg, William James, Kylie MacLellan, David Milliken, Paul Sandle, Elisabeth O'Leary and Alistair Smout; Writing by Estelle Shirbon; Editing by Kevin Liffey)