"All the problems with wind" is a bit of an overexaggeration. In fact, the video nicely shows how resilient it is. For instance, the first clip is of a wind turbine on fire. Notice how the rest of the wind farm is not on fire. The wind farm would have perhaps lost 2% of its capacity, but it has resilience in numbers.
To start with, yes, I think the UK needs new nuclear capacity - we need *something* that's not coal that is good at doing baseload.
But on the other hand: from the point of view of the National Grid, wind does have certain advantages:
* Each generator is small and there are an awful lot of them. A generator or two going offline doesn't cause sudden capacity problems. However, a large nuclear generating plant going offline suddenly can cause a huge power shortage that can be solved only by shedding load (in other words, blackouts).
* The wind, over a period of the next few hours, is pretty easy to predict. The wind doesn't just suddenly and unexpectedly stop blowing. You can pretty much say the wind will be doing in 10 minutes time what it's doing now, and if it's not going to do that (e.g. due to the passage of a frontal system) you can at least know what it's going to do. Not so with a large powerplant which may suddenly go offline with no warning.