So, I thought "X is a Y pub" meant that pub X (e.g. the Star) was owned by the Y brewery (e.g. Fuller's), and that Fuller's choose someone (well, usually two someones, usually two married someones) to run the pub. The brewery/pubco also usually exerts some control over which beers can be sold in the pub.
But now I learn that the Ship and Whale in Rotherhithe is "a Shepherd Neame pub, but they don't own it" (the manager of the pub told me this, in an email so I can't have misheard him).
Also, the Wheatsheaf on Stoney Street certainly appears to be a Young's pub, but according to an advert in the August/September 2008 London Drinker, it's also claimed by the Red Car Pub Company.