What was the main reason Britain expanded their empire ?

Becuese it wanted the riches of the lands that it colonised, just like all Empires.

Because, even hundreds of years later, we still hadn't gotten over being abandoned by Rome. We wanted to be an important part of a great impressive empire again, with power and status. Not just a pissant little backwater country. So we made our own. And no one was strong enough to stop us.

Because Western Europeans at the time believed themselves to be superior to all other non-white people. They believed it was their "duty" to conquer others who were inferior to "civilize" them never mind that countries such as China, India, and even the people and culture of the America's and Africa had culture long before Britain was even part of Rome.

The reason in one word - racism.

Geostrategic trading bases.

Then,geostartegic military bases to protect overseas trade.

for shits and gigs