This is a millennium-spanning question, and a complete answer would require a full discussion of English history with lengthy digressions on Magna Carta, Oliver Cromwell, and the Glorious Revolution. I can't speak with precision to those issues. What I can speak to is the modern apparatus defining the roles of the two houses.
Political Culture
The quick way to answer your question is to point you to the The Parliament Acts. But before we get there it's worth talking about political culture. If you (like me) are an American, you're familiar with a politics and political history where tactics that are legal, but never used out of custom or respect, eventually are used (paraphrasing Jonathan Chait). This is an ancient trend: American politics are often constitutionalized, with major action occurring when actors find and strain against the limits of the law. Only rarely are written norms transcended, or reimagined, and even then, they still operate in the background.
England is different. Because there is no written constitution, the normative force that keeps politics within traditional democratic values is the process itself. You'll see some examples of this as I continue, but here's a representative quote from a recent Commons debate implicating constitutional values:
[I]n many sophisticated societies—we are one such—those propositions are defended by a Bill of Rights, which is an entrenched statutory provision policed by a supreme court. We do not have that. We must rely first on the other place [Lords] and secondly on our sense of moderation.... I think that majorities should be chary about imposing their views on other people.
So, if you go looking for an ironclad law that keeps Commons supreme above Lords, you probably won't find what you're looking for. Instead, you'll wind up back where we started, at political culture. To the extent that it exists, though, the document delineating "which House got which power" is the Parliament Act of 1911.
The Parliament Acts
In 1911, Commons and (after much debate and royal threats) Lords passed the Parliament Act of 1911. This act, given royal assent by King George V, provided that:
The 1949 Parliament Act modified these rules by lessening the delay period. In other words, Commons' ability to legislate without input by Lords was accelerated.
Despite their monumental nature, the provisions of the Parliament Act are very, very rarely used: in fact, the Parliament Acts have been invoked just seven times since 1911. In the interim, Lords has not developed a tradition of stalling to the maximum extent allowed by law, and Commons has not developed a tradition of ignoring Lords outright. Instead, Commons appears to take Lords input seriously. The Parliament Acts were most recently used in 2004, to secure the passing of the Hunting Act, which limited the traditional nobility pastime of fox-hunting. Even the majority party, Labour in Commons, balked at using the Parliament Acts to force passage of a nonessential, fundamentally culture-related bill. See the Commons record, here:
As my hon. Friend knows, I have been in this House a long time, and I realise that invoking the Parliament Act is a question of judgment; that judgment is based on the importance that we attach to the issue in question. In my view, this issue is nowhere near important enough to justify invoking that Act.
It is clear that there is a strong divide between the two Houses. I am not a great supporter of the House of Lords; indeed, as my hon. Friend the Member for West Ham (Mr. Banks) may know, I voted for its abolition. But the fact is that we have it, and its current role is that of a second Chamber—a Chamber that is perhaps a little more thoughtful and which takes time to contemplate issues. [Interruption.] That has always been its role. Given our current constitution and the fact that we have not abolished the Lords, we should listen to it very seriously when such disagreements arise.
My great worry is this: after today, when will we next use the Parliament Act? Will we use it when another such issue arises?
I realize this excerpt is from 2004, but I really hope you'll bend the 20-year rule for it. It's an important insight into your question, and is essentially a modern discussion of a 1911 rule of law. For a source and discussion following largely the same trend but older than twenty years, see the last source added here, which discusses the 1991 use of the Parliament Acts to secure the passage of that year's War Crimes Act.
Lords Today
All of this leads to the conclusion that except for sui generis issues, the Parliament Acts created, and the House of Lords has accepted, its role as an "upper" house that is nonetheless subordinate to Commons, and useful mainly for deeper looks into tough issues that might not befit a majority-rule chamber. This is a valuable role that should not be lightly overlooked.
Sources