OP, first, stop panicking.
The govt advice is only what some of us who live 10 hilly miles from a supermarket, have been doing for years. The world won't end.
In my 40 adult years, I've been snowed in twice for a day each time. We've had one 4-day power cut, one 7 day powercut, I've had a central heating boiler fail at 7pm on Christmas Eve, and I've had the main house fuse blow half way through cooking Christmas lunch.
Plus I got covid and couldn't go out for a week, and a similar bout of real flu. But that's in 40 years.
On each occasion I coped despite living in the middle of nowhere as a single mum.
My basic kit is bottles of water, UHT milk, coffee, pasta, pasta sauce, rice, lentils, tins of fish, veg, beans & fruit. Chocolate to keep DS happy. A rechargeable lantern for each bedroom, and the sitting room, tea lights/hurricane lamps as back ups, and a log burner, matches & sufficient wood.
If you don't have a log burner and the power fails, you can go to a friend or relative who has power, or somewhere public that has a generator.
The govt is not talking about armageddon, just to keep you & your family comfortable for the time it would take to get enough emergency food and water to you.
I volunteer for a parish council and we have emergency plans and funds to support people in the community if extreme weather/power outages cause issues. We did it during covid, distributing food to vulnerable people sheltering at home, and we can do it again. Honestly, try not to worry.