How many times have Europeans tried to invade Britain

The pre-history ones are uncertain – following original nomads in perhaps 10,000 BCE, other groups moved in. These left no written record and it is unsafe to describe them as Celts, as that represents a culture (including language from which Gaelic, Welsh, Scots originates). So the waves of invaders/settlers is subject to speculation, linked to the artefacts they have left.

Julius Caesar invaded in 55-54 BCE, imposed tribute and ended the Britons supporting their cousins in Gaul against Rome. He left them to self-rule.

The Romans under Claudius took possession of England in the 1st Century CE, leaving at the beginning of the 5th Century CE as the western Roman Empire was disintegrating.

The Romanisd kings left in control used Germanic tribes of Angles, Saxons and Jutes as mercenaries. These tribes then took control.

These were followed by the Norsemen who raided and then occupied large areas, principally in the east.

Further Norse invasions culminated with William (a Norseman = Norman) and there were spasmodic attempts threatened by France, Spain (Armada), France again (Napoleon) and Germany (Hitler).