One of the surprising results of 9/11 and its aftermath was the support W got from Tony Blair. Tony Blair is the leader of the socialist Labour party. The natural position one would have expected him to take would have been with all the anti-war anti-american leftwing partys all over the world. In the immediate aftermath of 9/11 the Queen ordered her marching band in front of the palace to play the Star Spangled banner which was unprecedented. The flying of the US flag. Also unprecedented. And then the special memorial service at St. Pauls cathedral which the Queen and Blair attended.
I'm not saying the Queen can order her PM to adopt a policy. She is supposed to be above politics in theory. However it would not surprise me that she had a VERY strong influence on how Blair would deal with the US after 9/11. It would have been very interesting to have been a fly on the wall during her chats with Blair after 9/11 She is not without influence and background power and now 50+ years on the throne and dealing daily with PMs all through that time would definitely give her a strong hand. Like someone said she was a military mechanic in WW II and is clearly not someone who has forgotten what the US did during that time. It seems France and Germany have.