Interestingly it turns out you're a net oil exporter but only by a very slim margin. You export only about 100,000 barrels a day. So bravo. I'm still not sure about refining capacity but You're still fucked. Oil's the easiest, and hey, in that case you're sitting pretty. However that doesn't change anything I said about the rest of it all. Again, look at food. How long can you get by on just what's in your house right now? How much food is actually at your local grocery store? I've worked in a grocery store before. There is next to nothing (comparatively) "in the back". How many people use that grocery store? How long do you think it'll take them to clear it out?
Again, the problem is that you've got about 72 hours between normal and complete collapse of society. "We'll scavenge France." You're actually better off than I thought you would be. The problem still comes down to time. With no fore warning you're looking at a good 24 hours of everyone standing around, thumbs up asses trying to figure out what the hell happened. After that you've got to start getting trucks together to move on your plan. And it's not just trucks, you've got to get guys to move the goods from the stores/warehouses into the trucks. Guys who are at the moment scared and worried for their families. You've gotta truck into France (thank you Chunnel!) find stores, empty them into the trucks, and head back, distribute the food, and turn around. And the problem is each trip is longer than the last. Plus, you've got the same situation everywhere, 72 hours of food is about all they've got on hand. You've got serious issues with recognizing the problem, organizing the solution, physically getting to food stores in France, and working out distribution before your populace realizes there's an issue, which they will pretty quickly when all the restaurants close up (even less food on hand than most stores) and the markets are getting wiped out by people more on the ball than they. When they look in the pantry and a can of peas, two cans of soup, and a bag of crackers is the sum total of all food they currently have or have means to get, they're going to get desperate, FAST.
Medicines, you're going to have more on hand than food, but every pill, every dose is quickly going to become precious. While you will no doubt start to pillage pharmacies and hospitals you're going to still be having to scavenge, not produce. And there's there's the issue at it all. Production. The means of production are scattered across the globe with massive amounts of tribal knowledge and experience being wiped out. Even if you could secure a means of production you've also got to establish resources to it and then distribution from it. And how do you fix something when it breaks? You've got a plant that can produce asprin. AWESOME! A great basic medicine with many uses. What happens when the Samsung supplied PLC that runs the pill press has a fault? Who's going to fix it? What if it needs a spare part? It stripped a gear that was manufactured by Doosan in South Korea. Do you see the issue? Even if you can scavenge stuff to keep you afloat in the short term how do you re-establish in the long term? Modern society works because we've been able to specialize. We've got supply chains built that involve most of the planet The benefit is that a plant with a few dozen workers can supply an entire country with asprin, but to do so they're relying on thousands of people in other plants doing other jobs in other countries to get what they need to make it work, and so on and so forth.
The UK isn't some little backwards nation. There's sixty million people here in a modern industrial / post industrial society.
Which is actually the entire problem. You're a post industrial society with a knowledge and skill base that reflects that. Lemme put it to you this way. Your local powerplant, do you think it's all locally built? It's not. In fact I've had to deal with, "Buy American," initiatives before and it always came down to this, "We can buy American, or we can keep the plant running. Pick one." It's almost impossible to secure domestic boiler tube anymore. Most boiler tube is made in South Korea, France, Germany, or China (which is all shit). Controls? German. Flow sensor? Italian. Pressure switch? Canadian. PLC? Korean. Turbine? German. And I can go on, and on, and on but that's just end parts. That's not even getting into how those are built, and by who, and where. What happens when you blow a tube that you don't have parts on hand to replace anymore? You can scavenge, sure, but boiler tube isn't permanent. It's rusting, degrading. In about two years all boiler tube stocks that aren't stainless steel are going to be useless. You have to start making new. Well, the foundries are in other countries. Even if you did have people who knew how to operate them you still have to provide them with power (in another country) massive amounts of it, and raw materials (likewise in another country) to get ready to make the tube. And that's just dumb steel tubing. Hell, most sensitive electronic parts that make up a power plant aren't going to last more than a year or two unattended. The plants that make them, even less so. The modern power industry can survive because while a plant might only need to buy one or two pressure switches a year, once you combine every plant together you've got enough demand for pressure switches to keep a couple manufacturers in business making them. That's how it goes for everything in these plants. The plants are able to stay running because of a massive support infrastructure. Remove the infrastructure and you can't keep them running. Even scavenging will only keep you in business for a couple more years. Now change "power plant" to canning factory, or textile mill, or pill factory, or whatever.
Even if you could scavenge enough food out of Continental Europe (and that's really the only place you've got a chance of doing it) you're just delaying the inevitable. There's not enough time, or land, to plant sufficent crops to sustain your population and you're not going to be able to keep the machinery to move the food operating even if you could. Simply put, the population will rapidly shrink. As medicines run out and can't be replaced mortality rates from otherwise survivable diseases will skyrocket. Cancer paitents will die when drugs either can't be secured or can't be spent to keep an unskilled laborer alive. You're going to see starvation eventually. A massive uptick in violent crime.
Here's what's going to happen, best case scenario. Shit goes down, everyone else is dead. For about 24 hours no one has a fucking clue what's happening. People start to figure it out, the government gets it's head out of its ass and starts to organize. The trucks and ships start rolling towards the contient and descend like locusts on it. We'll assume things go perfectly and distribution works. People are fed, but people also aren't happy. They're not starving, but they're getting whatever happened to be in cans as fresh food goes away after about a week. Politicians start to listen to the engineers and realize they can't sustain society. Every underpinning is exactly one wrong part breaking from going down. Possibly permanently. Even if things can be jury-rigged you've only got so much time before something unrecoverable breaks. You have to use that time while scavenging is still successful to begin to educate your populace, 90% of whom have no useful skills in this new reality. Things like basic first aid, farming, animal husbandry. You might convert printing presses to cranking out "Survival 101, How Not to Die" as fast as they can. People are going to have to move. You'd start to pre-plan communities, portioning out critical professions like doctors, farmers, and such and providing them with groups of what will wind up being laborers. These groups will be sent out to existing farming communities across the continent and even the US, might as well restart the colonies, but with a preference to where you can grow varieties of food. Most of these colonies will more or less be abandoned at this point, on their own to survive or die. A central nexus of communities will be formed, really I don't know where, but someplace where you can grow food, catch fish, etc. This will be the center of the "Empire." By decommissioning most of your power plants, oil rigs, and other vital facilities you can take steps to secure the decommissioned plants as spares for the few you keep running. This central core's job is going to be to preserve knowledge, secure valuable equipment from across the globe, and try to force start the industrial revolution all over again.
If everything goes perfectly you can probably avoid the worst of it all and save most of the population. You're going to lose a lot of people to sickness and disease, see some communites collapse because they can't make it as farmers, etc. but that's just a hazard that you can't do anything about. If you do things right, spread people out far enough but not too far, you can probably avoid major casualties. If things don't go perfectly, if people riot or refuse, if the government delays too long, well, it's going to get ugly, fast. Given my general view on humanity, I suspect it'll trend towards the ugly as people are going to have a hell of a time adjusting to the change and most will likely refuse at first.
No country in the world, not the US, not Great Britain, China, Japan, no one country has any hope to sustain anything resembling modern society in this scenario. You're going pre-industrial, probably not too far, but you're going to go pre-industrial and there's nothing you can do to stop it, only delay it a bit.