No "cups" in old British recipes I've made but there will be measures you have to look up like a "gill".
Old family recipes would just say things like "add flour" and that amount was taught face-to-face and hands-on where you added enough till it looked "right" because onions and eggs etc. were not a uniform size.
This reminds me of a boxed item I bought ages ago where the instructions were basically: cook to desired doneness, season as desired.
Also reminds me of a coworker in a restaurant in Palo Alto who, when I asked him the recipe for a dressing I needed to make, told me "ginger juice, lemon, and just make it good". It turns out there were a few other ingredients.
And yeah, depending on how far back you're going or what sources you're using, there will be a lot of vaguely defined quantities. Glen of Glen and Friends on Youtube regularly cooks vintage recipes and gets into how things evolved over time. Most of his old cookbooks are either Canadian or American but from time to time he cooks from UK cookbooks.
I'm sure there will be examples and my childhood memories won't be great but that link isn't a good example of British recipes.
Most of the instances of "cups" come from the "Edwardian recipes" which is a collection of international recipes including American. It includes in the preface a Table of Measures which is what you do for Brits who see "cup" and ask "what the fuck is that?"!
British recipes today largely use metric units. Pre-metric recipes absolutely did use cups (although this persisted in Canada and the US more than the UK). As Glen points out none of these British cups were standardized.
How so?