British Isles is a useful, but under-used geographic term. The Open University uses the prefix CE (Continental Europe) for students who are not resident in the British Isles.
In formal writing, I’ve sometimes used the vague, but handy cultural geography term, ‘Global South’, which became popular in academic circles and differs from the geographically precise southern hemisphere.
For some reason, the use of the term “the mainland” triggers a certain type of Brit.
It’s far easier to get prostate cancer (even if you are a woman) than it is to get French citizenship. Boom, boom.
Look at the UK economy, it’s only a matter of time 
And, I believe, is a geographic term which does include the Island of Ireland.
Ha ! I live in Corsica and the French are referred to as “Pinzuti” or “Continentaux”! I like to remind them that I am not from the “continent” but from the other side of it!