Britain was never conquered or invaded. It did not come into existence as a country until 1707, with The Act of Union with Scotland. It was invaded in 1745 by Prince Charles Edward Stuart but he was not successful. There was an invasion by the French around the end of the eighteenth century. They did not get very far either.
The Channel Islands were occupied by the Germans in World War Two. That was the only part of the country that was invaded in that conflict.
The famous Norman invasion of 1066 was only of England. Scotland was not invaded then.