Hey Andrew,
Wondering how you got on with your issue if you are still reading this thread? My curiosity has got the better of me, I’d be happy to help further if you have any more info.
I finally got around to this (other priorities got in the way). I’m not entirely sure if the issue is fixed, but I suspect I am on the right track and wanted to share my story for others.
Please note I sometimes referred to 2015.10.0.2505. This is wrong. It should have read 2015.10.2.2505. Apologies if I mislead readers (my 3:00am brain).
When I installed the full installer fresh for 2015.10.2.2505 and before rebooting, I noticed the network status indicator in the system tray got an exclamation mark, indicating no internet connectivity. At this time the browser broke as expected, and so were nslookups through my local DNS forwarder. When I rebooted, the indicator returned to normal, but I still had no ability to browse. Uninstall, and browsing returned, even before reboot. So it’s not the upgrade from 2015.10.0.2504 breaking.
The exclamation made me think that there’s something going on in the network stack, which makes sense since Avast does some low level driver stuff. I found the version of Atheros AR8151 PCI-E Gigabit Ethernet Controller was about 2 years older than most recent, so I downloaded the driver from the motherboard manufacturer, rebooted and tried again.
Installing 2015.10.2.2505 fresh again this time did not cause an exclamation, and after reboot I was definitely able to browse, but it was very flaky. I suspect I was having other browsing factors during this test, but if gave me some confidence there was a network driver conflict earlier. Being 2:00am I didn’t want to diagnose further so I rolled back to 2015.10.0.2504 and have set aside some daylight hours to test again with less network congestion.
If you hear nothing more from me on this test, it means it was successful, and the lesson will be to check your network driver is current!
This issue affected both of the PCs with this onboard network card. So Andrew, if you are still having issues, have a look and see if all your affected sites also share the a common network interface manufacturer (eg, Intel and Broadcomm are quite common even for different motherboard manufacturers).
This was corrected by Avast https://forum.avast.com/index.php?topic=171939.0