neither lifts nor mobile phones can be relied upon in the case of a non trivial power cut
Absolutely. However the same might apply to fu;l fibre products as well - see below ...
Fortunately, the chances of significant losses of supply are reducing as fast as market forces are encouraging the UK supply industry to invest ...
Quite the reverse ! Market pressures - specifically for lower costs - are actively reducing the level of redundancy in the network. Instead there are moves towards things like interruptible supply contracts (ie pay large industrial users to shut down) instead of putting in/maintaining redundant capacity to cater for (eg) a circuit fault.
I recommend a read of this : https://www.raeng.org.uk/publications/reports/living-without-electricity
The subject of what happens to mobile networks is covered - they stop working ! In practical terms, the cost cannot be justified of equipping all base stations with anything more than a token battery backup, nor is it physically or financially practical to have standby generators available to roll out to them all.
What is clear from the report is that it was lucky that the outage was relatively local - had there been a widespread problem then the generators brought in by the DNO (ENWL) could well have been needed elsewhere.
Now back to the telecoms network itself. IF the connection goes all the way back to the exchange with no active equipment then it should keep going as BT exchanges normally have some very large batteries to keep everything running. But if there are any active devices in the link (like there are the green cabinets in FTTC connections) then it's questionable whether these would hold up for any sensible time (or at all) given the ongoing cost of maintaining batteries at every node. AIUI the NTEs used to date in all-fibre connections have a backup battery to maintain POTS service for a short time (hours) in the event of mains failure. I could well see these becoming a maintenance problem - will they ever get changed ?
That's the key benefit of the current copper based POTS lines - very reliable and completely independent of mains power (including powering basic end user terminal) for quite some time.
Nothing insurmountable, but it WILL add costs (eg periodic battery replacements) to various applications.