Wind varies a lot. On May 4th in the UK it was generating nearly 9GW, but on May 1st was generating 220MW.
Over the last year it's generated 15% of the UKs electricity demand, so increasing by 10 fold would mean it could generate everything, if there was infinite storage.
Lets assume we start off with 100 lots of South Austrailia batteries - so 13 GWh of storage, and fully charge them on May 13th 2018 at 22:30.
After 40 minutes we've added 5.5GWh, but we've taken out 12GWh, and in the next few minutes it stops.
OK, lets go for 130GWh Storage - or 1,000 SA batteries.
That's great, we're doing well. Until May 14th at 07:50, when the battery is full, so we throw away the energy. That's great, we can last until May 17th - less than a week.
So we start with a battery that's got a total capacity of 10,000 SA batteries - 1.3TWh, and starts off full.
Unfortunately on June 1st it wasn't very windy, and we've been drawing down on our batteries for 2 days. The lights go off on June 1st at 10:50.
For the UK to be wind powered for the last year, we'd need 1) 10 times the current wind production 2) A battery or other storage capacity of 13 TWh -- that's 100,000 batteries the size of the one Musk delivered to South Australia.
Or 1) 100 times the current wind production 2) A battery or other storage capacity of 300 GWh -- that's 2,500 batteries the size of the one Musk delivered to South Australia.
Or 1) 1000 times the current wind production 2) A battery or other storage capacity of 500MWh -- that's 3 batteries the size of the one Musk delivered to South Australia.
I'm not sure if it's possible to get 1,000 times as much power from wind as we currently do (21TW of production, generating 57TWh over the course of the year), but it would generate an insane amount of excess energy at windy times.