Uk does actually follow EU regulations and standards because all the technology is designed and manufactured in the EU. HS2 is being built to an EU standard loading gauge with EU standard electronic signalling, likewise crossrail. When routes are upgraded to electronic signalling they are upgraded to an EU standard signalling technology, likewise with electrification. Loading gauge is typically smaller but when new bridges are built they will try to aim for the largest EU standard loading gauge that’s practical. The reason why you can’t easily run a night train from Edinburgh to Paris is not technological it’s because the customs and border requirements necessitate an expensive building like an airport to house them. It’s not true that the EU rail system is homogeneous either, e.g Belgium, Germany and France all have electrified lines running at different voltages which can require bi or tri mode trains for through running.

> Whereas on the Continent, trains regularly cross between countries and the whole system is much more-but far from entirely -integrated, politically and physically

That's not true. There are some local connections and integrations, but outside of high speed rail which is generally built using the same standard, each country has their own load gauge, electrification standard, signalling system, etc. Cross-border trains are usually special traninsets built to multiple standards to be compatible.

There is progress on more integration and standartisation, and pretty much all new lines are built to the same standards, but the vast majority of rail is existing.