Re: Answering a few points in the comments...
There are several, unrelated renewable sources. The chances that they all fail - 100% - is infinitesmal.
Ah, variation of the "wind is blowing somewhere" lie.
While it's true that having wind AND solar AND hydro all at (or close to) zero at the same time are quite slim - hydro is only a small amount and so can be ignored in practice.
So lets look at what happens in the UK in (typically) late december. Solar is doing naff all - the days are short, the sun is low, so for probably something like 18 hours of the day it'll be producing nothing worth considering. So that leaves wind ...
Contrary to what the wind lobby claim, there are often prolonged calms that cover, not just the whole of the UK, but the whole of north west Europe. I recall reading an article (in print (IEE), some years ago, no I can't find it now) where it was pointed out that we have had periods as long as TEN DAYS with effectively no wind across the whole of western Europe. Pumped storage hydro and batteries aren't going to help with that - they'll run out in a matter of hours.
So while the backup needed isn't actually 100%, it's not far off.