If we’re to insist on it being a specific country’s food, it really should be Indian no? It was invented by Indian diaspora in the UK as (IIRC) a take on traditional Indian food using ingredients that are easier to obtain in the UK.
IMO saying tikka masala is British food is like saying General Tso’s Chicken, which was invented by Chinese diaspora in the US for similar reasons, is somehow American food. I don’t think the country it was invented in can really claim credit in either case.