Why have I got no British ancestry despite being from an Anglophone Caribbean country?

Not sure if to post this here or St Lucia forum.

Most of my family are of St Lucian origin, and we can trace part of our family history back to the mid 1800s, (however this is only the European side, not African, indigenous or Indian side).

My family only seem to have French and Spanish ancestry (some as recent as great grandparents) but absolutely no British or Irish ancestry. This doesn’t make sense to me at all, considering St Lucia was a British colony from 1815 until 1979.

I have also found that a lot of my ancestors born and raised in St Lucia migrated to France, Panama, Venezuela, Spain, Trinidad and vice versa (and even Louisiana!).

I wanted to know how common this is for St Lucians.