I don't necessarily doubt that, in general, Brits don't put much stock in the Special Relationship, but if that's truly the case, I have to wonder why it is so.
Too much time has passed for any gratitude or camaraderie (deserved or otherwise) that might have been a product of WWII to endure and have much influence on the nations' relationship.
I would think sharing a common language and heritage would preserve a bond that extends beyond mere sentimentality, and I suspect that bond is stronger than many would realize or admit, but it will take stress and shared fear to reveal it. Certainly not something to hope for, but entirely possible.
The US is currently going through some hard times, but so is the rest of the world. Predictions of America's loss of superpower status are quite premature, and europeans who secretly or blatantly hope the American economy utterly tanks just have no appreciation for where their own economic interests lie.
I suppose it's natural not to want to be the sidekick in a relationship, especially when you were once the hero, but to allow such silly notions to dictate foreign policy would not only be ridiculous but self-defeating. Fortunately for the UK, its leadership has not allowed foolish pride to come before a fall.
I guess much has to do with one's world view. If one believes that Europe is essentially immune from anything but isolated and comparatively minor terrorist attacks, who needs the US? Sure our intelligence is helpful, but our military might is not required.
The UK can do just fine on its own without kowtowing to the Yank bumpkins. A good friend of mine, a Scotsman in Chester, once assured me that the Brits could have turned back a Russkie invasion without, thank you very much, the help of the Yanks.
So many in this forum assure me that the days of American imperialism are numbered. If they are right, I sure hope, for the sake of the nation, that our leaders are smart enough to sidle up to the new Big Dog, especially if it shares our values (It's pretty damned sure it won't share our language or heritage).