Oh yes, absolutely. "The bedrock" is what defines the culture.
But it's quite a vague predictor for whether you're going to build a good business together; or whether your jokes about other cultures or sex would be perceived as racist, ironic or simply a matter of pragmatism; or what is acceptable as part of your personal life.
Honestly I find the perceived notion of having a shared culture is detrimental to actually realising that you disagree on many deeper important issues.
For example, many of my current middle-class co-workers were quite surprised by the results of the Brexit referendum, while it wasn't that clear to me as I've spend a fair amount of time in Leeds hanging out with the working class or working for a few supposedly full of middle-class media agencies. They didn't tend to be too humble to share what they actually thought of being a part of the EU, while they were quite humble at sharing this with their friends (shy tories, etc.?).
Besides, I would never agree I know British culture in it's full depth. It's funny you mentioned "fork handles"/"four candles" - which is exactly the thing a friend of mine said this weekend. I just Googled it. A culture enthusiast would follow this up with a binge of the show.
But this still does not make a foreign speaker seem more genuine if he suddenly starts speaking northern accent, uses common grammatical variations (I was/I were) or borrows from a local vocabulary. Neither does it do any good for someone northern to come to London and try to negotiate a contract with someone of South African descent without any appreciation for a more common pronunciation or cultural grounds (although well - aren't they both practically British?).