I'm not so sure I'd go with "strong" ally, they have some proving to do.
As for the shoebomber, I think you'd agree that Britain has been a strong ally for real...for real.
But are they secure? They fostered a lot of the terrorism through harboring the Finsbury Park Mosque ( both the shoe bomber and Moussaoui were nurtured there). The London Underground bombers were from......Britain.
I'm not saying Britain isn't our friend, I'm saying they sometimes have screwed up badly. Do you want screw-ups doing your security?
For sure...for sure. But that support of course came after the Revolutionary War and the War of 1812. And I do remember reading once that the British Admiralty in the 1920's had drawn up plans for war with the United States over trade issues.
Many of things that are cited against the UAE occurred before September 11, 2001.