"Chicken tikka masala is now Britain's true national dish, not only because it is the most popular, but because it is a perfect illustration of the way Britain absorbs and adapts external influences." - Robin Cook, 1946-2005.
The problem is that traditional British foods, like Cornish Pasties, pies and Yorkshire Pudding, are not the most exciting fare, and I say that as a fan of my examples. We Brits, however, were fans of meat and gravy and when Indian (or in the case of CTM, Bangaladeshi) cooks started selling their wares, it didn't take long for a Glaswegian Bangaladeshi to make meat and gravy for his customers and lo, the Chicken Tikka Massala was born. It is so popular in the UK because it is traditional meat and gravy (with the side order of stodge being rice in this case as opposed to pastry crust or potato) with a hint of our multi-cultural roots.
I think it's as traditional as Fish and Chips, a dish no-one disputes as traditional, in spite of its recent age. If 1860s is traditional, so is 1950s.
Oh, and if you want the finest Curries in the world (yes, even more so than India for our westernised pallets) then I would recommend Glasgow first, Birmingham second and then the usual Bradford, Leicester, Nottingham, etc., options. London is nowhere near the finest.