Unless you have a backup generator for your premises, keeping the ability to make non-mobile 999 calls in a power cut needs a Battery Backup Unit (BBU) - a box with a rechargeable battery in it, and the electronics to keep it topped up when the mains is on, and to manage the output to the router or ONT.
These units are commonly used for computers, so there are lots of models available. But the computer units have a rather different need - they need to cover a substantial power drain (PC and monitor) but typically only for a few minutes (to allow the user to shut things down properly). To protect your telecoms equipment, you need a box that can provide a relatively modest amount of power, over a much longer period of time.
Ofcom have set requirements for VOIP companies to offer a battery backup unit to customers in certain categories - more details here - but I cannot find any sign that any telecoms providers are currently (Aug 2023) actually doing this. But you can buy a unit for yourself, of course.
BT (via their EE shop) currently offer a "one-hour" unit in two variants, both costing £85. The version for "full fibre" (or FTTP) presumably has capacity to power both ONT and router, but this is not totally clear. The other version is for those whose connection is via copper wires, at the same price - they don't make clear whether that lasts longer (because it only has to power your router) or whether it has a smaller battery in it. In August 2023 they said that they could order these units for you "on demand", but don't say how long it would take. When I checked again they did have them in stock. Just 10 of them. Then they ran out again.
Independent company Simple Telecoms are offering a (one-hour) 12v backup unit at £40. TalkTalk appear to have been supplying similar (identical?) units for a trial of battery backup to FTTP customers in 2022, but there is no sign of any broader roll-out.
The important thing to understand is that the equipment on digital-only phone lines will use pretty much the same amount of electricity whether you are making a phone call (or using the internet) or not. So you will be running down your backup battery from the moment that the power goes off.
I would be looking for an eight-hour battery. Nobody is marketing a battery for telecoms use with that capacity, but there are units for computer backup that are big enough to provide this. In time, appropriate units may be specifically marketed as being suitable - for now, I guess the answer is to talk to a specialist supplier. But it is really not good enough that consumers are having to do research or make guesses as to what they need to respond to a long-planned technology change.