Hi! I travel two/three times per year in UK, not London but Manchester area. My understanding of their legislation is
slip joints and friction folders are OK to carry. Also these ones anyway have a
limit on blade length (3 inches = 7.62 cm). When there, I normally carry my SAK Spartan but e.g. I have to leave home my SOG/FOX multitool since the blades and tools are locking ones.
As a general rule, when traveling in Europe and going into
urban areas it’s custom to avoid public display of any blade. This is also recommended in UK. I always keep my SAK loose in my pocket. My own experience is, if one behaves respectfully and politely and practice situational awareness, there are really very few chances to get into trouble. Anyway, like it is for most of other European countries, Police has the right to stop and search anyone even without a specific reason. Specifically for UK, I found this:
https://www.gov.uk/police-powers-to-stop-and-search-your-rights
It’s very similar to what’s happening in Italy as well. In Manchester area, I personally never had issues with carrying and using my Spartan discreetly to peel an apple or cut a sandwich in the streets, public parks, etc. Even if the law might allow this (
I don't know), as a rule of the thumb, I avoid using my own EDC in public places (e.g. restaurants, pubs, shopping malls, supermarkets, etc.). Be aware there could be some stricter rules/laws specifically for London Municipality, this also I don’t know. There are many Fellow Members from UK here who can surely better help. As a foreigner myself, this is my personal take and experience with UK legislation in this respect.
Hoping it can help.