This is somewhat of a "where do you draw the line" question. One could say that the national dish should comprise of things we used to eat i.e. are native to England. In that case, Turnips should be out, as they were introduced here in 1700. Rabbits were introduced here in the 1st Century AD; if that's long enough ago then you could include them. But if you're looking at things native to this country then no.
It seems then, that the national dish should be determined by its popularity and not its origin. If we look at that, then chips (according to a YouGov poll) are the most favoured, followed closely by fish and chips. Bit of a rubbish poll though, as vanilla milkshake comes out as number 19. Must have been completed by youngsters.
If it were up to me, I would say it's the food you'd most likely eat for a treat or special occasion. In which case it would be a roast dinner, or F&Cs, or curry. A lot of the older generation doesn't like curry (weirdos), and again that generation would have had F&C as a staple because it used to be cheap. Which just really leaves the roast dinner - a regular favourite but also not a cheap treat. People would, and still do, work extra hard to save up so they can afford a joint of meat at the weekend. That is the answer