A nice summary of the different styles of pool in Britain by the BTCV can be found here.
The fact that a pond with no connection to a river is full of fish is certainly notable, though fish quite often seem to land up in water bodies that seem pretty inaccessible. The usual explanation is that they are dropped by birds, though eels have been seen migrating across land**. Another possibility in larger bodies of water is a population surviving as the water system changes. For example, although not isolated from rivers and the sea, Llyn Tegid (Bala Lake) in North Wales, has sufficiently cold water to mantain a population of European Whitefish known locally as Gwyniad*, which were probably present in Britain at the end of the last Ice Age (~18-10000 years ago) but were competed out, or died out, in warmer and more accessible waters elsewhere.