The Commons is badly out of touch and represents the views of the politicians and not the people. I could probably come up with at least a dozen areas where a referendum would go in a totally opposite direction to 'the will of Parliament'.
The Lower House is filled with party favourites; lickspittle clones of the party who offered them the chance of a seat.
The present system produces ever more lawyers and professional politicians when we need the people's voice to be heard. Our current crop of politicians believe they have a patrician function.
What would pull these wretches up in double quick time would be if a certain number of signatures on a petition were able to produce a referendum on a political issue, as is the case in Switzerland which has recognised the weaknesses of so-called democracy in a modern world.
As for the Lords, you can reform it but how would you improve it? The political parties would continue to put forward the people THEY want us to vote for.