LONDON (Reuters) - Britain is facing the biggest terrorism threat in its history and has foiled around 40 major plots since suicide bombers attacked London in 2005, Home Secretary Theresa May said on Monday.

The government would on Wednesday set out new laws to take on the militants, May added, including legislation making it easier for security services to track attackers online, and check if radicalized fighters were flying into Britain.

"When the security and intelligence agencies tell us that the threat we face is now more dangerous than at any time before or since 9/11 we should take notice," the home secretary (interior minister) said in a speech.

Insurance companies would be barred from providing cover for ransom payments under the new legislation and airlines would be banned if they failed to provide information on passengers flying to Britain, she added.

The government has said Britons returning from fighting in Syria and Iraq provide one of the most serious threats.

May said around 40 terrorist plots had been disrupted since four young Britons carried out suicide bomb attacks in London in 2005, killing 52 people.

These included attempts to conduct Mumbai-style gun attacks on British streets, blow up the London Stock Exchange, bring down airliners and murder a British ambassador and military servicemen, she added.

"Almost all of these attacks have been prevented," said May. "But ... the terrorists only have to be lucky once."

Planned new measures include giving police the power to seize for up to 30 days the passports of British and foreign nationals suspected of traveling to take part in terrorist-related activities, said May.

The new laws will also make it easier for police to identify who is using an Internet service at any given time.

London's top police officer on Sunday said authorities are increasingly worried about a "lone wolf"-style attack and have foiled four or five plots this year.

On Monday, Mark Rowley, Britain's top counter-terrorism officer, said police were "stretched" but had stepped up their efforts, making 271 arrests this year. Warning the threat would remain high for several years, he said the public's help was needed in spotting potential attackers.

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Around half of Britons traveling to Syria are newly radicalized and not previously known to police, Rowley said.

"I would never use the word inevitable but of course ... terrorists do sometimes succeed," he added. "We are going to do everything we possibly can do to stop that happening."

Britain raised its terrorism alert to the second-highest level in August, saying an attack was now "highly likely".

(Reporting by Andrew Osborn and Kylie MacLellan; Editing by Stephen Addison)