The problem with the Lords is that they are effectively a retirement home for time-served politicians (discounting those given special privilege to be there), we didn't elect them, and so logically they do not represent us. The Lords are a historical hangover, just as the Monarchy is, but we like the Monarchy, they are cute and British, they bring in tourists, even if they are an elite institution funded mostly by the tax-payer.
At the very least the Lords should be regarded as an advisory body, with no power or authority to hold any sway over the people we have elected to represent us.
To advise, yes, to persuade, yes, to enforce parliament to take a vote on matters, no. Their powers should be limited in a way that is similar to the monarchy, historically relevent and that's it, we could save a few £millions a year also.
Only publicly funded elected representatives should be making decisions on our behalf as we have entitled them to do so.
It's not really a case of 'be careful what you wish for' more a case of 'it's time we changed an institution that is no longer fit for purpose and no longer serves the voting tax-paying public effectively', as with all changes there would no doubt be unintended consequences that we will just have to live with.
Brexit highlights the constitutional issues the UK has with dealing with matters that represent the modern political world we live in, the times they are a changin', the slow barge of institutions should also be upgrading their engines to keep pace.