Sometimes a product will tell you--mostly when it's trying to convince you it's organic or a health food. They they will list safflower oil or the like.
The pubs and restaurants are very helpful, though. Britain has a lot of vegetarians and other heath-food aficionados, and they will go out of their way to make sure you get what you want to eat. One pub cooked me a ham and egg supper with no oil, and a waiter at Heathrow airport went back himself to check out the oil in his restaurant's kitchen (it was soy, darn it.)
We had two suppers at the pub pictured, with the kitchen staff making my chicken one night and trout the next was made with with butter or olive oil. Another day we had a wonderful lunch at a little cafe next to a train station where the proprietor was Spanish. She made us a Spanish tortilla with salad and potatoes, all with olive oil. She said she had had a customer in the day before with a soy allergy, so she was already familiar with what she could serve and what she could not.