Ten thousand years ago the UK was covered in glaciers and no freshwater fish could have survived. At the end of the Ice Age the glaciers retreated northwards, but the only way freshwater fish could have recolonized the country would have been by following immediately after the glaciers in the meltwater (unlikely) or crossing the sea some time later. To cross the sea they would need to be able to tolerate salt water.
Hence the number of freshwater species of fish in the UK is likely to be very small.
It is. There are 57 species, only 43 of which are classed as native, compared to 13,000
The Romans invasion and later the feudal/monastic fish ponds of the twelfth century onwards may have led to an influx of new species. I wonder how many of the 43 native species were established over 2000 years ago.
[See Maitland & Craig in Silent Summer: The State of Wildlife in Britain and Ireland, ed. N. Maclean, CUP 2010.]