They mostly do have the V label on vegan products.
However some just have it stated somewhere near the ingredients as "suitable for vegans" and then there's also some where they don't state anything but they are still made to a vegan recipe. But for the most part, at least for the kinds of things tourists will buy, you won't have to deal with the third one that much, if at all.
You'll be able to find loads of vegan restaurants in London via Happy Cow. It's been a few years since I've been down to London so I don't have any current suggestions. I do remember hearing there's a market (i think Camden) where there's a shop for vegan artisan cheese and that it's amazing.
I went to London last year and have a few suggestions for some great restaurants:
Purezza in Camden: Great pizza, pasta and desert like Tiramisu
Unity Diner in Whitechapel: Amazing vegan meat and cheese (burgers, fish and even steak)
Oowee in Brixton: Not really a restaurant but a fast-food joint. Imagine a completely vegan McDonalds.
If you like fast food, you can also go to an actual McDonalds, they have a great vegan burger there that's only available in the UK (McPlant). Enjoy your stay!