Wine is a drink made from the fermented juice of fresh grapes. A wine takes its name from the country it comes from. Simple! So 'English Wine' is wine made in England from the juice of fresh grapes - and English Wine is generally excellent quality. But, you may be surprised to discover, it isn't 'British Wine'.
A legal curiosity means that wine-type-drinking-products made in the UK, or Ireland, from non-fresh, imported, grape juice can't be called 'wine', but they can be called 'British Wine', which sounds odd, but probably harmless. For a century British firms have been using this curiosity to make somewhat suspect imitations of sherry and port, but they've always sold it cheap so it hasn't really mattered too much. But from time-to-time it stops being harmless. As the grape juice is usually imported as a concentrate it's up to the makers to dilute it with water as much as they like - and dilute it with water they do. And because it isn't really 'wine' it isn't covered by the strict EU wine-making rules, so, having diluted it, the makers can bulk it out with as much sugar as they fancy. You can make a weak, thin, tasteless liquid, put it in bottles labelled 'Merlot' or 'Chardonnay' and sell it for, oh, just a little bit less than the real thing, and get away with it - as long as the small print says 'British Wine'.
If you'd like some more confusion, there's a difference between ‘English Sparkling Wine’ and ‘Sparkling wine from England’. We'll let the Consumers' Association explain https://www.which.co.uk
A popular sherry-style fortified British Wine
Bensly's British Wine Vault
Cheltenham Chronicle - Thursday 20 October 1814
See: Made-Wine