I have caught several 20lb+ carp out of rivers mainly the Thames, they are easy to catch the hard bit is locating them. If you find a spot then you are assured that 500 other people have as well and then its difficult to get in the swim, they are not feeding due to huge amounts of bait being thrown in.

I personally know of at least 2 people who have caught 30lb+ Carp from the Thames as well. Lots of articles on the net about it plus some nice videos on youtube. One article saying that the EA had found in one stretch of the Thames that Carp out numbered other fish 3 to 1.