Apologies that this post is resurrecting the dead, but I want to provide an update for anyone else who has this problem and finds themselves on this forum page.
After a reinstall of the OS, the issue of frequent, random BSOD went away, but the system crashes again if I have an active device connected to either of two out of the three USB ports on the laptop. By "active" I mean a hardware device that runs software through those ports (I'm sure there's another, correct term...!)
For example, I use a mobile broadband device to access the internet (a Huawei HiLink E3131 modem), and if its in either of those 2 ports the system crashes within about 10 minutes; similarly, a smartphone connected to the PC through that port and syncing with the PC will also cause the BSOD before very long. But a USB memory stick used to swap / save files has no impact. The third USB port is fine with the smartphone and modem - I think that port is USB 3.0, and the others are both USB 2.0.
So perhaps there is a driver issue with those two USB 2.0 ports, or perhaps any attempt to send large volumes of information through those ports eventually pickles the system... or maybe something else to do with the ports is buggered. Anyway, my work around for now is to just not use those two ports if I can help it. Which is a pest, but seems to prevent the crashes and isn't the end of the world.
If anyone knows what might be going on, I'd be happy to hear!