MBP crashes when using browsers

Haven't found precisely this problem described before...

At random, my MacBook Pro will crash completely - black screen, no response whatsoever - when I am using an internet browser. As far as I can tell, it only happens then, but it makes no difference which browser I use. I can't recognise a pattern otherwise (other actions, specific websites, whatever).

Sometimes it reboots by itself, sometimes it gives me the multilingual "computer shut down incorrectly" message, sometimes it does nothing and I have to force restart using the power button.

Similar problems have been reported on here and traced to magnets (none round me), dodgy battery (I'm nearly always running off mains AC) loose connection to the screen (I'm not moving or even touching the screen when it happens), and so on, but these appear not to be relevant in my case.

I'm running El Capitan 10.11.6 on a 2011 MBP, but this problem predates my OS update - it happened already on OS 10.6. It has got more frequent recently though. Wondering if this is a known problem, whether there's a fix, or whether my Mac is just getting old.