Pure hipster-ville man.
I live in New Cross, which is south east. And there is a pub called The New Cross Inn that has bands playing. I think Discharge were due to play there recently. It's pretty small. New Cross itself is pretty small though. In east... I have no idea. It's hit & miss. Most places I know are going to be full of hipster types. Old Blue Last, The Macbeth. They're around Old Street/Shoreditch.
In Soho there is always 12 Bar and Crowbar, and Garlic & Shots. I generally just end up at places where bands are playing or where my mates like to go. Sam Smiths owned pubs... pretty cheap.