A private members bill is one where a single MP introduces a potential law on a subject he feels strongly about. They usually have zero chance of actually becoming law, but they establish a principal, and often end up prompting the Government into action.
I’ve ranted here an elsewhere about the issues with royalties on streaming and how generally rubbish they are. The Brennan Bill (Kevin Brennan MP, not the hard drive music storage thingy) is the first shot across the bows of the rights holders. It’s not perfect, and some, but not all, of the BPI’s objections are valid. This is an area that needs reform soon.
The NME have written about it in simple terms here
Digital Music News gets down in the weeds a bit more here
In the meantime of course you know that Bandcamp is the place to buy music and support the artist. The last Bandcamp Friday is this week. Their sales grew by 122% in 2020, and probably more this year… You know it makes sense.