Thanks for the answers to my questions.
Gum color is normal which is good. No pain when you palpate Alfie's abdomen is good; if he were experiencing a bladder obstruction, then I would expect him to be quite uncomfortable when you feel in this area. But, knowing when he last urinated can help to take this problem off of the list.
Whether or not the vomit you found is related to his current behavior will be hard to assess since it doesn't take much to trigger vomiting in a cat.
The following are going to be the most common causes for a sudden change in behavior such as you're seeing.
1. I do understand about not having a thermometer but if you manage to get your hands on one, then it will be very useful to know if he's running a fever or not. Normal is between 100 and 102.5. If it's normal, then we can take this off of the list of possible causes for his behavior but if it's high, then we'd have to wonder why.
The possible explanations include a bacterial infection, especially if he goes outside (he could have gotten into a tussle with another cat or critter and has an abscess) or viral infection.
There is a condition in cats that is called Fever of Unknown Origin--this is exactly what it sounds like which is that we can't find an explanation for the elevated temperature. Treatment is primarily supportive which consists of fluids and drugs to reduce the fever. Most cats recover very quickly.
2. Pancreatitis can happen very suddenly; these cats just stop eating and can become lethargic. About 30% of cats with this condition will vomit.
We don't have a good explanation for why this condition develops either.
We do have a test for this (spec fPL) although I've come to doubt its reliability in some cases; treatment consists of fluids and pain medication (we believe the pain is why they stop eating).
3. There are, of course, any number of possible reasons why a young cat might vomit but when they are also lethargy and don't want to eat, then I'd want to include a foreign body or possibly dietary indiscretion on the list.
4. Some cats will just have "off" days and return to normal within about 24-36 hours and we're none the wiser as to why. I suspect a viral infection in these cases but have yet to provide it.
I can provide over the counter options for nausea which may help if this is contributing to his behavior. Famotidine (aka Pepcid AC) can be given at a dose of 1/4th of a 10 mg tablet twice a day but may be hard to find in the UK. Another option would be Omeprazole at a dose of 1/2 of a 10 mg tablet once a day.
Maintaining hydration with water or Pedialyte is important, especially if there’s a fever. You can dribble this into the side of the mouth with an eye dropper or syringe every several hours if he's not drinking on his own. You could offer tuna or clam juice or low sodium chicken broth to tempt him but I wouldn't want him to drink a lot at one time (since it might stimulate more vomiting if he's really nauseous).
If he continues behave as you describe, then a vet visit may be prudent.
I hope this helps and that you see improvement soon. Deb