The Battle of Hastings was close but in the end, Harold of England was killed and the Saxon army fled.
William took the throne. In 1072, he moved north to stop the frequent rebellions of the Anglo-Saxons.
The conquest of Wales took a long time. It finished in 1282 during the reign of King Edward I. Edward also tried to take over Scotland but did not really conquer it. Scotland kept a separate monarchy until 1603, and did not unite with England until 1707.
The Battle of Britain (or Operation Sea Lion) took place when Luftwaffe (a German) tried to gain air superiority over the Royal Air Force (RAF).
The objectives of this attack were: to neutralize the RAF so future attacks on the British Isles could be made, destroy airplane production, to attack places of political significance, and to terrorize the British people.