As LondonAnalytics pointed out, it mostly isn't at present and doesn't have to be pumped storage.

That cost might be a bit high if it's only a matter of extreme peaks and troughs, a few hundred hours a year?

I think using interconnections for smoothing can be cost-effective in times of less extreme wind peaks and throughs, too: that would still mean less use of gas. This depends of course on how much of a phase shift there is between wind peaks and throughs passing the western shore of Ireland and the Netherlands (at least).

_{*Lunatic*, n.
One whose delusions are out of fashion.}