BT have announced that they are planning on ceasing all landline services by 2025. They are currently consulting with communication providers about the switch-off.
While many have already switched to mobile-only communication from home, and probably VoIP communications from the office, there is still probably a fair number of people that use their landline - even if only occasionally.
The plan isn't to cease to-the-home services altogether. Instead, they will be switching over to use internet-only lines (and therefore VoIP phones). For anyone still using a phone plugged into the wall, either handsets will need to be replaced with internet-capable ones, or there will likely be the option to plug existing handsets into converters (this may require them to be plugged directly into the internet router or special wall sockets). An internet connection will be required to use any "landline" phone from this point.
What isn't yet clear is whether this will mean it'll be possible to remove line rental from the equation altogether. At the moment, everyone currently has to pay for line rental, even if they never use their landline. There's no technical reason for this. An internet connection would work fine without it. It may be that this switch-off will see an end to this anachronism.
(Updated August 2021 to include the option of using existing landline phones with converters).