This to me is a little bit silly. The partition of India was in 1947 (a British idea) and Bangladesh didn’t gain independence from Pakistan until the 70s. Before that, the entire thing was “India” and we still use the term “Indian subcontinent” today to refer to the entire region.

The partition didn’t happen along culinary lines, so I don’t see a reason why it would be inappropriate for a restaurant for a restaurant run by Bangladeshis to claim it serves “Indian” cuisine within the general meaning of the word.

If you go to a Bangladeshi restaurant in the UK and ask for authentic Bangladeshi food, most often they will be happy to serve it for you.