For periods of low wind you either need services that you can shut off (as we already have for industrial users), power that you can ramp up (as we currently have with gas), storage of some form (as we already have with pumped hydro) or interconnectors to an area that does have wind or other dispachable power.
Nuclear doesn't do any of that. All it does is provide a base of power that can't go up or down. It can exist alongside other low carbon power sources but it doesn't compliment or assist them.
In the future, in the UK, we will have more not less demand for constant supply. High energy users such a electro-arc furnace may fit such a use that you describe, but they are less common in the UK these days. The future is electric transport: so cars getting charged on an evening, more trains getting electrified, commercial vehicles running on electric.
Last I read, the estimated demand for vehicle recharging would be about 5GW on the grid.
Wind cannot cover this, as the highest demand (as I said), is usually in the depths of winter. A deep freeze event lasting weeks would render the UK without power, or being overly dependent on Europe for imports of electricity. You cannot import wind energy from other areas of the UK if the whole of the UK is without much wind which is not unusual in a deep freeze situation.
People will still need to heat homes, to charge vehicles, to use computers, and more essential needs.
We need nuclear power, because wind/solar cannot provide baseload power, and we will always need baseload power, because the real world demands constant supply, even without electric cars. With a future of decarbonising, that will increase.
Thinking that wind will do it doesn't make it so.
Edit: I should add that we should not need to go down the route of "For periods of low wind you either need services that you can shut off", when we don't need to. Aside from the economic hit (huge), it would would be morally wrong when we have alternatives. Also would be political suicide, and rightly so.
The baseload supply issue is not going away.