Well... was Britain particularly prone to outside invasions? Just look at some of the other areas in the immediate vicinity. France was 'invaded'* by the Celts, Romans, Franks, Vikings and later the English. Iberia has historically been invaded by the Celts, Phoenicians, Greeks, Romans, and then multiple waves of Arabs and Berbers. Greece, in the past, saw invasions by the Persians, Celts, Romans, Avars, Slavs, Bulgars, Arabs and Turks. And the list goes on.

Of course there are also areas that have been invaded much less than Britain but the point stands. Britain is not uniquely prone to invasion in history. It's just a place with decent farmland that people can reach without too much trouble, and that occasionaly attracts new people. Someone could probably write an interesting piece about the common discourse of Britain as a land that saw a lot of people wash over it, for example the ever-popular "English is just three languages in a trench coat" meme, and how that reflects on people's understanding of its history, but I'm not qualified to do that.

*Obviously, when we're talking about things far in the past like the bell-beaker culture or the arrival of Celtic culture in the British isles, describing it as an invasion is controversial since how either of these things happened is still heavily debated, but for the sake of the question I'm rolling with it.