Interesting question.
There are clear and compelling reasons to go with 1066 as it very much shaped the way the country was governed and the language that we speak today. However, Britain is a country that had gone through wave after wave of invasion, each of which shaped who we were to become.
Certainly the Black Death had a major impact and shifted a lot of power from the ruling classes and landowners back to the workers who could now have more freedom to choose where they worked and who they worked for.
The Reformation had a huge impact on British identity and culture. It also played a major role on the preservation of language - the Welsh translation of the Bible in particular.
The execution of Charles II. Yes, the royal family was later restored, but it would never again have the same powers. The erosion of royal power was not an overnight event though - it had been gradual over many generations.
Similarly the Industrial revolution. The inventors, scientists and industrialists of that era made a massive impact on Britain and the world. It led to a huge shift from rural to urban living for millions. It also led to misery for millions due to slavery, child labour and the exploitation of the working classes. It also lead to massive advances in road and rail that still impact on our lives today. We are still driving on many of the roads built at that time, living in the houses and using the sewage systems.
More recently advances in vaccines and medicines and in science and tech have also shaped who we are today.
However, almost everything I have listed is not unique to Britain. We do not live in a bubble. Things that happen here are also happening throughout the world. World Wars, scientific advances, attitudes to human rights - these are all defining moments for most (often all) other countries too.