On my kitchen scale one cup converts to about 150 grams. But baking is a pretty precise art, so a measurement of one cup is pretty vague.
King Arthur Flour has a great weight chart. Sorry I am on my phone so I can't give you the link...
It really depends on the flour, how its packed, etc. fyi from a weight perspective 150 gm is a little under 1/3 lb. If you are baking cakes in The USA, I suspect that your flour will weigh a little under 150 gm per cup. Annoying, I know. But sadly volume based measurement systems and weight based system go together like oil and water!
You should be able to get your hands on a measuring cup that is calibrated in cups, liters, ounces, etc. I've seen these measuring cups in Germany, so I am sure a good kitchen store in the UK would stock them as well. That might help, but I have converted most of my baking recipes to ounces or grams to avoid using cups. The Joy of Cooking, a standard US cookbook, has an excellent chart that compares the weight and volume of various ingredients. I used that as the basis of converting my recipes. Also, you can try plugging what you are looking for in the Google search box and most likely an answer will pop up--type, for instance 1 cup all-purpose flour in grams.
It depends on the density of the ingredient. One cup of granulated sugar, for example, weighs 7 ounces, or 200 grams. A cup of flour weighing about 5.5 ounces converts to 150 grams because it is less dense.
1 cup is 237 mL; I'd just use a 250 mL cup and take out 15 mL (1 tbsp).