It really depends on the restaurant. I'd not expect a fast food chain like KFC or a Frankie & Benny or Pizza Hut to be able to provide a pint of milk. They work within a range of fixed parameters and don't really have flexibility to go "off piste", and usually have to buy everything from the "approved" suppliers if not get stocks automatically ordered via the franchise ordering system based on till sales etc.
But anything half decent, like a privately owned restaurant or a good independent pub/restaurant, should be able to, as they're usually a lot more flexible and more likely to have management who have the discretion as to what they order, where they order it from, etc., so will probably have a broader range of stock in the kitchen, including drinks.
It's a bit like wanting to "customise" your food order in a chain - if, say, they have chicken with one kind of sauce, and beef with a different kind of sauce, they look at you as if you're an idiot if you ask for chicken with the sauce that comes with the beef. Yet in a private restaurant, that's usually not a problem, even asking for options that aren't even on the menu is often possible.
I appreciate where people are coming from as regards stocks held, but realistically, any half decent establishment is going to have extras of staples like milk - they'll be going through many "pints" of milk in a day (probably dozens), so their stock control really won't be so fine-tuned as to run out of milk for coffees if they "sell" a pint to a customer.
I think if they refuse, it's more likely down to "computer says no", i.e. they don't know how to run it through the till, rather than them genuinely not having enough pints of milk in the kitchen fridge!!