In England you can EDC a "penknife", which is a folding blade less than 3 inches long. Locking blades are probably not considered penknives. Something like a Leatherman Juice would be OK under this rule; it has short, non-locking blades.

You can carry most longer or locking or fixed blades if you have a good reason. "To hurt people with" is not a good reason, even in self-defence. Taking a camping knife to a campsite ought to be OK.

Some knifes are disallowed completely on the grounds that hurting people is their primary use, eg flickknifes, butterfly knifes.

In theory it makes no difference whether the blade is part of a multitool. In practice the police might use their disgression, taking into account your general demeanour etc, and a multitool might fare better there. You are in any case unlikely to be searched unless arrested for some other reason, at least outside London. I've not visited London itself for many years so I don't know what is normal there, eg, whether museums and art galleries have any checks.

I currently EDC a non-locking SAK and an M4, which is a tiny multitool with locking blade. I'd defend the M4 in court if necessary, and hope to set a new precedent. I also usually carry a Juice. I've just ordered a Prybaby, which I suspect would be more useful for escaping from a train. I don't know if that will be light enough to EDC.

I'm not a lawyer.