The whole idea of a following the results of a non-binding referendum that 52% of the people that voted passed for such a major thing as leaving the EU seems quite strange to my American eyes. I would think something as major as joining the EU should have required a super-majority of people voting for it in and a super-majority to leave. Like a US constitutional amendment. I need to read more English history to understand how people think this is the way things should work.
Parliamentary Supremacy: Parliament has the last word on all constitutional matters, whether written or unwritten, and in any event can change any inconvenient aspects of the written constitution (e.g. historical bills and charters) with a simple majority.
Historically the House of Lords provided a check on populist sentiment in the House of Commons, but the powers of the House of Lords have slowly been diminished over the past century or two (albeit with their consent, more or less; but it's a one-way street), while also making membership more "democratic" and thus more likely to express populist sentiment.
> the powers of the House of Lords have slowly been diminished over the past century or two (albeit with their consent, more or less; but it's a one-way street)
In the most key point, decidedly less: “vote to strip your powers or the monarch will create enough new peers that will vote the right way that the measure will pass anyway” isn't real consent.
So total power, basically, but limited by custom and decorum. If Parliament says that the majority vote on a referendum with decide what they will do, then that can be the way it is. Parliament can also change its mind afterword and not do it, but that would be unlikely as it is not the expected way of behaving.
The details are specified in the specific Act of Parliament allowing the vote. The 1979 Scottish devolution referendum required a minimum 40% of the electorate vote Yes, so it failed, despite a 52% Yes vote, due to insufficient turnout.
