Re: And the house of lords?
Two problems with that:
Firstly the commons can invoke the parliament act and overrule the lords.This takes a year but is possible.
Secondly the government was elected with the referendum as part of their manifesto. By tradition (but not by law) the Lords doesn't block anything that was in the ruling parties manifesto. They can ignore that but to do so would risk their existence, you can't have an unelected house try to block something that the elected house made as a commitment in order to be elected. You could argue that the manifesto only promised a referendum, it didn't promise to act on the result but that's splitting hairs a little too thin.