Afaik we have/had a rather good range of resources in the UK and good production facilities until recently when all the steel plants started closing. The one thing we dont have is petrol but I dont think the UK could ever be made to starve, its not the same as starving a city in EU4 which in real life took many months anyway. There is no way you would ever starve a country. Yes we would have to change to horses instead of cars, tea instead of coffee, honey instead of sugar etc etc but a country like the UK could still last many many years if not indefinitely on its own. Its the luxuries that would have to go.
The reason Germany was near to collapse at the end of WW1 was more due to the lack of farmers etc as they all went to be soldiers. If you arent supporting a massive army and can rely on the navy and airforce to keep an army off your shore I think we could go on for years on our own if need be. We managed fine without much help in 1940. I think Churchill was being overly dramatic when he mentioned the U boats. More likely his job/career would have been on the line if he had failed to win the Battle of Britain - that was probably what he was scared of most!