I cant speak to the Brit's "homegrown" terrorist problem, but I do believe the US approach to terrorism has been woefully misguided for the past eight years.
IMO, a "war on terrorism" is no better than a 'war on drugs".....bombastic rhetoric that has no underlying strategic response and far too great a focus on military force...ie, the invasion/occupation of Iraq which by many measures only increased the world-wide recruitment by terrorists organizations.
The Rand Corp, a DoD contracted think tank published a report last year on "How Terrorist Groups End."
The evidence since 1968 indicates that terrorist groups rarely cease to exist as a result of winning or losing a military campaign. Rather, most groups end because of operations carried out by local police or intelligence agencies or because they join the political process.

....military force has not undermined al Qa'ida. As of 2008, al Qa'ida has remained a strong and competent organization. Its goal is intact: to establish a pan-Islamic caliphate in the Middle East by uniting Muslims to fight infidels and overthrow West-friendly regimes. It continues to employ terrorism and has been involved in more terrorist attacks around the world in the years since September 11, 2001, than in prior years, though engaging in no successful attacks of a comparable magnitude to the attacks on New York and Washington.
Al Qa'ida's resilience should trigger a fundamental rethinking of U.S. strategy. Its goal of a pan-Islamic caliphate leaves little room for a negotiated political settlement with governments in the Middle East. A more effective U.S. approach would involve a two-front strategy:
* Make policing and intelligence the backbone of U.S. efforts. Al Qa'ida consists of a network of individuals who need to be tracked and arrested. This requires careful involvement of the Central Intelligence Agency and Federal Bureau of Investigation, as well as their cooperation with foreign police and intelligence agencies.
* Minimize the use of U.S. military force. In most operations against al Qa'ida, local military forces frequently have more legitimacy to operate and a better understanding of the operating environment than U.S. forces have. This means a light U.S. military footprint or none at all.
Key to this strategy is replacing the war-on-terrorism orientation with the kind of counterterrorism approach that is employed by most governments facing significant terrorist threats today. Calling the efforts a war on terrorism raises public expectations — both in the United States and elsewhere — that there is a battlefield solution. It also tends to legitimize the terrorists' view that they are conducting a jihad (holy war) against the United States and elevates them to the status of holy warriors. Terrorists should be perceived as criminals, not holy warriors.
How Terrorist Groups End
The other focus that deserves far more attention IMO.....understanding and responding to the root causes of terrorism.