There are many non-native species in Great Britain, but only a small proportion are invasive. Having said that, some are causing increasing problems and the GB Non-Native Species Secretariat was set up to provide an information portal (much better that we could provide, so please go there for more information) and co-ordinate national action.
We do have problems on the Aire (most especially with Giant Hogweed, Japanese Knotweed, Himalayan Balsam and Signal (red-clawed) Crayfish. You can read what we are doing here.
If you are working, fishing, canoeing or otherwise 'messing about in rivers' then please take note of the 'Check, Clean Dry' advice on that page and help avoid spreading the misery around.