In the Vigor 2860ac in LAN > General Setup, I changed the For NAT usage IP address and the DHCP Server Gateway IP address to 196.168.1.2 as I wanted to use 196.168.1.1 for experimenting with another device whose web interface can't use another address. Initially this allowed me to continue browsing to the internet (using Virgin's superhub as modem) on the PC but the DNS appeared not to work for my iphone. I didn't have time for investigation so left it overnight. Next day the PC browser also failed to find web pages (possibly DNS cache kept it alive previously?). Changing back to 196.168.1.1 fixed it. So how can I change the address of the router to 196.168.1.2 ?

You are changing it in the right place. It should work. Sounds to me like the DHCP is handing out the wrong DNS, though that needs to be checked.

Is the other device a router or similar? If so it may be 'hijacking' your lan with it's own DHCP server?

Check primary / secondary DNS on LAN >> General Setup - LAN1 Details, if set they should be the same as the router IP (presuming you use the router as DNS cache as per default.
Check DNS setting midway down LAN >> General Setup, if set to force then it should be set to LAN1.

Can you "ping 8.8.8.8" from the PC cmd prompt when the problem occurs?

If problem occurs do IPCONFIG/ALL at PC cmd prompt and tee what is trying to use the old router address.

Thanks for the response. I wrote out a reply to this post having tried various things you suggested without success, then I reverted to 196.168.1.1 and did some stuff on the web. Before finally submitting I thought I would try it a third time. This time it is working! I checked access on a different PC and it still works. I surfed sites I'd never been to and it's still ok so DNS caching isn't involved. I'm stumped as to what the problem could have been. I don't like intermittent glitches but I guess I'll stick with it and hope it is permanently ok.

As a matter of interest, when it went wrong I suspected it was a DNS problem but when I pinged 8.8.8.8 I got "Destination Host Unreachable" so it wasn't even connecting to an IP address. Also it isn't the other device doing anything because I haven't connected it yet.

I will see whether it goes wrong tomorrow!

Ah... right. Well if it does happen again, with that destination unreachable, you should be looking at default gateway address(es) in IPCONFIG and maybe "netstat -r" to check the routing table, though that should be the same as the ipconfig.