My 20+ year old grape vine has mistakenly been cut back to a 1metre high main stump. Will it regrow?

Twenty years is nothing for a grape vine. They are still using some double that age for wine production in France. In fact, the normal treatment of vines is to cut them right back and only to fruit the new growth which is allowed to reach five or six feet maximum.
The only problem is that if it's been pruned at this time of year, rather than when it's dormant in the winter or early spring, it might have damaged its vigour, as it can cause bleeding of sap, and instead of the leaf energy being returned to the stem and roots, it's been removed with the prunings.
But I'm sure it will come back with no problems next year.

I agree with Bertiefox - I poisoned one in autumn 3 years ago - damned thing has just started growing again, and it was a woody stumped, 10 year old one.