So, nothing obviously wrong with the sequence of steps I took? The only thing that was different from the above, from memory, was the coding rate. As I recall, the default was 3/4 but somewhere I saw an indication that it should be 2/3 in Ireland. As it was a maximum value I opted to leave it unchanged.
I have since reverted to the Windows 7 drive and found:
1. The tuner was no longer showing up (at least, there were no terrestrial stations in the list of stations)
2. It was found ok when I rescanned the stations and correctly reported the identities of terrestrial stations as it found them
3. However, they (terrestrial channels) still didn't show up in the station guide / onscreen menu
4. Rebooting and removing the DVB-S tuner, then repeating step 2, resulted in a working live TV view -- the tuner works
I have certainly had both tuners working with Windows Media Centre in the past but I don't recall when the most recent occasion was.
It all seems a bit reminiscent of the days of IRQ conflicts needing to be resolved with dipswitches. I will try the DVB-T tuner with Linux (LibreElec) on its own, in case there is somehow an interaction / coexistence problem. All very strange! I have no idea why tuners that used to coexist would cease to do so. Must be something else, surely?!
BTW the output from dmesg once I installed the right firmware was
[ 13.458048] dvbdev: DVB: registering new adapter (cx88[0])
[ 13.458060] cx88-mpeg driver manager 0000:06:00.2: DVB: registering adapter 1 frontend 0 (Conexant CX24116/CX24118)...
[ 13.711565] dvb-usb: will pass the complete MPEG2 transport stream to the software demuxer.
[ 13.711773] dvbdev: DVB: registering new adapter (Hauppauge Nova-T 500 Dual DVB-T)
[ 13.721015] usb 4-1: DVB: registering adapter 2 frontend 0 (DiBcom 3000MC/P)...
[ 13.729661] MT2060: successfully identified (IF1 = 1218)
[ 14.331747] rc rc1: IR-receiver inside an USB DVB receiver as /devices/pci0000:00/0000:00:15.2/0000:05:00.0/0000:06:01.2/usb4/4-1/rc/rc1
[ 14.362432] Registered IR keymap rc-dib0700-rc5
[ 14.366098] input: IR-receiver inside an USB DVB receiver as /devices/pci0000:00/0000:00:15.2/0000:05:00.0/0000:06:01.2/usb4/4-1/rc/rc1/input15
[ 14.366186] dvb-usb: schedule remote query interval to 50 msecs.
[ 14.366190] dvb-usb: Hauppauge Nova-T 500 Dual DVB-T successfully initialized and connected.