Perhaps, but undoubtedly the most salient influences come from the values of the enlightenment, namely that:

• Everyone is born with the same rights and obligations, just by virtue of being human -- so no monarchs, lords and any other renaissance fair bullshit;

• The government exists for the people and by consent of the people.

I claim that these are values are still antagonistic to the current political system in the UK, and closer to the values of the EU, if we are being honest. Yes, I know that there are still other monarchies in Europe, but they are mostly ceremonial. We can pretend that the British monarchy is equally ceremonial, but that is pretty disingenuous. There is plenty of evidence that they still hold very real (unelected) power, and furthermore the entire English identity is still organized around the ideas of being "British subjects", something that people over there seem to say with pride. We just don't have similar values.