Having just checked a few things with a friend who is, in fact, moderately politically active, Labour do things more or less the same way. And, more annoyingly, I got a few things wrong.

Lords can't veto a bill, they can only delay it for a time and bounce it back to Commons. Also, apparently (and this is weird, since I clearly knew it because of all the figures I've seen come and go, it's an odd blindspot) Cabinet is not solely limited to MPs but may also include Lords as well.