What, pray tell, are they bound by?
Nothing.
Parliament is sovereign. Under the British constitution it is the ultimate authority.
Note - in saying that we need to be very clear on what we are talking about - colloquially, the House of Commons and House of Lords together are commonly referred to as Parliament, but when it comes to the constitution, there’s a little more to it.
That refers to the Crown-In-Parliament (or as the UK currently has a Queen, the Queen-In-Parliament) which is a union of the House of Commons, the House of Lords, and the Monarch - The Queen in this case.
This is the ultimate authority over British law. Acting together, the House of Commons, the House of Lords, and the Monarch determine what the law ultimately is.
The Monarch will generally do as the House of Commons and the House of Lords wish, and the House of Lords will generally do what the House of Commons wishes. There’s only limited situations governed by law and convention where the Lords can overrule the Commons, and even more limited situations where the Monarch can overrule the Commons and the Lords - but those limitations arise, because in the past both the House of Lords, and the Monarch have agreed to accept those limitations. If they had declined they wouldn’t exist (admittedly, some of those agreements were made under various forms of pressure - remember the House of Commons once executed a King).