Strange as it may seem,
fyrefli, I think you will find that you can hop on a train at Temple Meads and go to Newport (or take a flight to Dublin) with a similar lack of border paraphernalia. I agree with your observation of an "island mentality" that differentiates we Brits from continental Europeans, but that's because we
are an island.
A land border is intrinsically unenforceable - even the Berlin Wall wasn't 100% effective - and inevitably a rather artificial construct. Even if it follows a major river, only a rowing boat is required to bypass any possible border controls. An island, on the other hand, has well-defined, natural borders that are capable of being enforced, and many of our continental friends find that difficult to empathise with.
Happily there remain many cultural differences between neighbouring countries within Europe - try commenting to your Dutch neighbours on their similarities to the Germans, if you'd like to see an example in operation
