Sorry to bang on but I'm not confused about anything. You chaps need to go and read Part FCL, at least the bits to do with LAPL and PPL flying. The word currency is not mentioned at all, anywhere in the entire document. There are two sections with the words recency or recent in their titles. FCL.060 refers to carrying passengers, if you do not meet the recent experience requirements it is illegal for you to carry passengers. FCL.140 refers to LAPL holders, if they do not meet the recency requirements it is illegal for them to fly unsupervised. Those two sections are what is meant by recency.
The ratings on a PPL, CPL, MPL or ATPL are either valid or not. They are never current or uncurrent. None of the ratings laid out in Subparts G,H,I,J and K are ever referred to as current, they are either valid or need to be renewed.
The word current is mentioned four times in Part FCL, three times it is irrelevant for our purposes, the other time it's in the phrase "is in current flying practice". There is no legal requirement to have a proficiency check just because you are not current. There is a requirement for a proficiency check if your SEP rating has lapsed, ie is no longer valid, but that is not the same as currency. FCL.740 does not require your rating to be current, it requires it to be valid.
Currency refers to how much flying you have done recently (
). Referring to the two flights mentioned above, I was not current on the second flight because I hadn't flown it for six months, I was legal because my TMG rating was still valid.