The first time the Isles left the rest of Europe, was when the Romans departed. For about 1000 years they painted themselves with woad and ran about fighting.
When the Normans came in, the first thing they did was attempt to suppress the local feuds and create a country. During the successive reigns of Gloriana and James, it actually happened. If the effects of the continent were not real there would have been no Protestant Reformation, English Rennaissance, etc.
Ultimately, you are probably better off staying in.