From my own observation and research (mostly about making my home more efficient and weather proof), it seems to be the way rising temps will affect the UK and northern Europe will be
- warmer air holds more moisture
- melting ice caps means higher sea levels
- higher sea levels means rivers adversely affected
The end result is more rain, more dodgy storms because of hotter air and more flooding. It's not the Britain will become "like Italy" because we're too far up the curve of the Earth for that. More likely that we'll have more bad impacts.
For us to adapt it would most likely mean continuously repairing roads, weatherproofing houses, moving away from flood plains and building loads of defences. Costs a lot of money, either way.