You don't need a generator. You need a way of recharging essentials - there are many power banks available and if you google 'portable power station' it's easy to find some relatively easy solutions that will power things you need like phones, rechargeable lighting, radios etc for quite some time, and you can often also recharge these with solar too. You can get perfectly ordinary solar power banks for ~£40 which will at least give you a few phone charges if needed.
You need a way of eating if there is no power. For those with plenty of outside space that might be a stove powered by wood or something but for someone in a flat in London it probably just means stuff you can eat without having to cook it. Tins of soup, beans, sweetcorn, tuna, sardines, microwaveable rice/pasta, pasta sauces in jars etc can be eaten cold. Bread in the freezer (obv will unfreeze without power but once unfrozen will last a few days or longer). Maybe some powdered oat milk or something (am suggesting this because I have tried powdered cows milk and it was horrible). Only buy the tins if you'll eat them anyway, and just rotate and keep a stock in so you have at least some food for a short term difficulty. Think of three meals a day for three days to start with.
You need warm clothing and blankets in case it's cold. But most people probably already have these.
You need a torch or rechargeable lighting. Even a small torch (with some batteries) is better than nothing.
With respect to water, just put a reasonable number of large bottles of water in whatever storage you have and switch them out now and again. If you forget and it tastes plasticky, water the plants with them or save for washing in an emergency. You can also get water cubes that take 10L or more quite cheaply on Amazon etc. I have some in an Ikea Kallax storage unit, enough for water for my family for a week, and every six months (I have a reminder on my phone), I use them to water the plants and refill.
Have a bit of cash available in case banking systems go down. Appreciate this is difficult if you are not comfortably off but some is better than none if it can be done. And it might be useful in a more ordinary emergency, like just running out at the end of the month (put it back when you can).
Nobody is talking about a full on nuclear bunker. But it's sensible to have a bit of stuff available in case there is a problem. There are plenty of European countries that recommend that their citizens do this on a regular basis.
@Uricon2 I don't know how critical your husband's bed is in terms of his comfort or survival, but the portable power stations I mentioned earlier can power these if you get a powerful enough one. My dad has one for my mum because she is more or less paralysed and if the power went out she could not eg sit up to eat since her hospital bed is the only real way of her being able to do this. We bought it a couple of years ago and have used it several times in power cuts. It is great and holds its charge really well.