I'am on the other side of the Atlantic but I would like to see how british doctrine differs from american doctrine. One issue you always must take into account is the size difference of the 2 forces. Their is going to be a natural difference.
If your interested their is a site AEI, Its a US think tank. They video archive and post transcripts. They did a series on the future of each of the services. The army and the marines had a lessons learn panel. They touched on counter-insurgency doctrine somewhat .I can't remember exactly what was said .It was a while ago. Transformation is the overarching process. It involves a number of different Items. Doctrine is just one of the Items. I can give you links if you want .They are all day conferences and you would have to sift through several panels to find what you may be interested in.