As part of that fight, the government is putting forward a new tougher antiterrorism bill intended to close what London sees as gaps in the laws.
The government maintains Britain needs the new categories of offences to enable the police and courts to apprehend and try terrorists before they commit their crimes. And also to stop extremist clerics from preaching that incites others to terrorism.
But the new bill is getting only lukewarm welcome by some experts.
One is professor Paul Wilkinson, who chairs the Center for the Study of Terrorism and Political Violence at the University of St. Andrews in Scotland.
"It sounds to me that if it is applied as a general tool for use in terrorist cases, then it might well be useful," Wilkinson says.
Other experts are more skeptical. Some point out that the new categories of offences that are being introduced -- such as "acts preparatory to terrorism" or "glorification or condoning acts of terrorism" -- already exist under previous provisions.
Professor Bill Bowring is a legal expert at London's Metropolitan University.
"'Acts preparatory to terrorism' is already covered in the terrorism legislation, and particularly in what's recently been going through on control orders. Exactly those phrases," Bowring says.
Bowring adds that the new legislation may not be much better than the existing one. It is allegedly so imprecisely worded that it could implicate some organizations that have nothing to do with terrorism.
"I think the criticism in general is that the definitions are so broad in the legislation from the year 2000 onwards that in principle the activities of Amnesty International and Greenpeace are caught by the antiterrorism legislation," Bowring says.
Doug Jewell is a spokesman for the National Association for Civil Liberties. He says his organization is looking forward to studying the new bill's proposals in detail. He also maintains, however, that there is no need for them, as there are already similar clauses in the existing legislation.
"Our view is that Britain already has a whole raft of legislation capable of dealing with preparing, plotting, conspiring to cause terrorist offences. So, we would be very interested to see what is actually in the new [category of] offence," Jewell says.
Jewell also disagrees with some other elements in the proposed legislation. One is to replace the current burden on courts to show proof that is "beyond reasonable doubt" with a lower-threshold definition of the burden of proof as a "balance of probabilities."
He says this has already happened anyway to the detriment of the fairness of court proceedings and must not be made part of the new law. "We're very concerned at this particular proposal. We were amazed to see it in the Labour Party's Manifesto, and we feel it is a very broad power, which will lead to miscarriages of justice if it is actually put on the statute book," Jewell says. He adds that he hopes "wiser heads will prevail."
Professor Bowring is also critical of this proposal, saying it could be against current European legal standards.
"For criminal offences that would be an extremely serious backward step. It would be part of the restrictions on right to jury trial, and the restrictions on the right to silence. To have any lower standard of proof in criminal cases would be very dangerous, and would almost certainly also violate the European Convention on Human Rights."
Some other legal experts seem to support Bowring's view. For example, Jane Henderson, a law lecturer at London's King's College, has told RFE/RL that the "balance of probabilities" proof for criminal cases would be "extremely harsh and against British tradition."
Still another element in the proposed legislation is to review the operation of "control orders." These measures enable terrorist suspects who have not been charged with any offences to be tagged, monitored, and have their freedom of movement restricted.
Wilkinson says he doubts whether the "control orders" have really worked and what the proposed changes may do. He says that some of the measures -- which require very demanding police supervision -- would be hard to properly enforce and supervise.
"You would have to also sever communications with the outside world, so there would be no telephone, there would be no computer -- quite comprehensive isolation of an individual. More importantly, I think, this is what worries the police, the houses would then become magnets for supporters of the people who have been detained," Wilkinson said.
And Wilkinson stresses that this could lead to tremendous disturbances and a security threat. "A bit of a nightmare for the police," he concludes.
Bowring says that in "his own personal view" the existing criminal law is "absolutely sufficient and effective for combating terrorism."
It remains to be seen whether Parliament will share all these concerns and what changes it will make before the new bill becomes a law.