The United Kingdom has its roots in ancient history.

The only time we have been occupied / ruled by a foreign power was by Rome, way back about 2,000 years ago. They just withdrew when their empire collapsed.

We were conquered again in 1066 by the Normans but they really just merged with indigenous peoples, so they didn't remain a separate power.

There is, therefore, no-one from whom we ever became independent and therefore we have no day similar to your Independence Day.

References to November the 5th and the Gunpowder Plot have nothing to do with independence whatever.

There was an occasion when King Henry the eighth declared a kind of religious independence from the Pope, but that is not noted as a special day.

It might help to know just what your research project is.

Anyway, good luck with it.

EDIT.

I should add, I think, that the UK is actually a quite uneasy alliance, with different areas having very different histories.

Scotland and Wales, particularly, resent the English and many would like to claim independence from England.