Chocolate syrups, the kind you put in coffees etc. and can buy at your local coffee shop, are almost always vegan. You can make hot chocolates from them and there are tons of brands, including Sweet Freedom (an entirely vegan range).
Whittard even do different kinds of chocolate powders that are vegan (some of them aren't, however, you need to check).
Or I just buy vegan chocolate bars/buttons and melt them down. Dark chocolate bars, the kind you can buy in corner shops, are often vegan. But Aldi also sell a 60% chocolate bar which is vegan, too. Montezuma do a 54% vegan chocolate.
Plamil sell 'chocolate flakes' that are ideal for melting into warm mugs of vegan milk. Their range is entirely vegan as well.
Yeah... I've never had issue making a vegan hot chocolate.
I am pretty sure Cadburys Cocoa is vegan but I admit I have not checked. But yeah there are a lot of chocolate non-dairy milk. I seem to recall that the alpro choc milk was quite thick - I often would dilute it.
I've found Sweet Freedom Choc Shot Liquid Chocolate. It's lovely. I have two teaspoons with one teaspoon of agave syrup and a tiny dash of milk. Tastes very chocolatey. I suppose you could add it to Oatly to make it more intense. Apparently it's for all kinds of uses, including having on toast or fruit. Of course I found it in Holland and Barrett, it would be hard to be vegan on the Isle of Wight without H&B.
I bought some raw cacao (£5 for a massive bag from Costco) and mix it with some warm almond or non-dairy milk. I also discovered you can put powder in a Nespresso milk frother which makes the best hot chocolates ever! Much cheaper than buying individual packets