Is it permissible to bring a bottle of wine into Hyde Park ,or any park in London for that matter, along with your lunch?

Since most parks have cafeterias that serve beer and wine, it would seem reasonable that you could byob.

Champagne picnics, long summer evenings, of course.

If you need more assurances than that it seems reasonable and that m kingdom would do it, "The Royal Parks and Other Open Spaces Regulations 1997" do not prohibit the consumption of alcohol in the royal parks.

I would and have brought a bottle of wine with our suppers in the park. While the Royal Parks may have regulations on the books regarding alcohol consumption, they are not enforced. On any summer (or spring, or fall, or winter) day there will be many people enjoying drinks in the park.
Just don't drink from the bottle or leave it in the paper bag.

You'll be happy to hear that nowhere in Europe has 'open container' laws like the States.

We *are* adults, no need to be puritanical about life's little legal pleasures . . .

Evening picnics in Holland Park during opera season, oh yes. Also thinking about Hyde Park when the Red Hots are playing this summer!!!
Enjoy your dejeuner sur l'herbe !