Yep, even when things are running normally, 6hrs is going to be on the cusp of where it's worthwhile to leave the airport IMO.
I'd be using the broad line 1hr through immigration, 1hr to get to where you want to be, 1hr to get back to the airport and leaving 1hr to get through security, to your gate and a bit of contingency. That means you'd have 2hrs tops in London.
Is there something specific you want to see or do?