In Britain, people from both places will leave their shoes on indoors at home, praise the NHS, watch football and think the queen is fine.
This is by no means a universal thing here!
And yes, even the queen is not universally accepted. Famously, the Labour party used to be republican, but seems to have mostly given up on that plank of policy.
In any case, my main point was that intense local rivalries exist, but actual differences between neighbouring places are typically fairly minor.
This can go very deep because as you know (but may be surprising to our American friends) in Europe we have much less cultural uniformity.
For example, in the two towns in Central Italy that I'm thinking about, which are only 15 km apart, people speak completely different dialects that are only partially intelligible one another.
A fun fact is that now I live in Australia which is one of the countries in the world with the least variance in accent. You can't tell Sydney and Perth accents apart, even though the two cities are thousands of kms apart.