And let's not forget the running joke of "sock it to me" on the Laugh-In TV series. It developed into a long series of near-rhymes and puns and invariably ended up with someone getting a pie in the face or a dousing with water.
Random gleanings from 19th C and early 20th C. sources.
Sock was 19th C. Eton slang for "edibles of various kinds privately imported." Etonians also used it as a verb for "to eat," especially food eaten outside of regular meals.
>Hotten says the word is still used by the boys of Heriot's Hospital School at Edinburgh, and signifies a sweetmeat being derived from the same source as "sugar." "suck." Swedish sock "sugar."
A "sock shop" was a place that sold food.
At Winchester:
>to hit hard especially at cricket. It also means to beat or defeat in a game. "Sock" is a provincialism meaning to hit hard, but much used by slang-talking people
It is "old cant" for a pocket. "Not a rag in my sock" is BE for penniless.
"To sock" is an Americanism for "to smash a hat over head and ears." Also called "to bonnet."
There is a false etymology that sock,+ "to hit," came from +sockdaloger.+ (American history and/or trivia buffs will recognize "you sockdolagising old man-trap!") +Sockdologer is "1. a decisive blow or remark 2. an outstanding person or thing."
The etymology of sockdologer is unknown, but it dates only to the early 19th C.
Thanks again for all that input. I was using the article with a new student of mine. In the event, one of the few words he didn't have major problems understanding from that article was the word ...'schloss'...
And he told me he regularly peruses the The Telegraph :)

Max Hastings is simply referring to Boris's well-reported history of having affairs. If his way of saying it sounds a touch, or even more than a touch, politically incorrect, well that is consistent with Max Hastings having said it.
I think sometimes words get around precisely because they have more than one resonance.
Although I think it is irrelevant to the present question, (and apologies for wandering off in this way if it annoys you) but I'm interested to speculate whether Boris would use the word "soccer" for the game most - but certainly not all, or perhaps not all the time - British people call football (other than in specific contexts, for example he played at a Soccer Aid charity game).
Boris went to Eton, which has a curious relationship to the game. It is one of the few Public Schools to play (Association) football rather than rugby. But they also play a unique Eton variant of football known as the Field Game, and for that reason Association football at Eton is often referred to precisely as Association (full stop). Now soccer is precisely a coining derived from Association, like rugger from rugby, which is the kind of turn-of-the-century (19th to 20th) upper class slang that falls comfortably from Boris Johnson's mouth. Unfortunately I no longer have the company (to my knowledge, anyway) of any tame ex-Etonians I could put such a question to. A relation of mine was a teacher there, indeed just at the time Boris was there, but he passed away some time ago, unfortunately very soon after retiring. Oh the things I would have asked him if he had stayed around long enough for his significant former charges to become apparent.
"Now soccer is precisely a coining derived from Association . . . "
Apparently because Association+ was commonly abbreviated +Assoc. and spoken as such.
I didn't bother to include it, but a number of those 19th C. books I looked at talked about "socker" as "Association football." For example:
>Socker (public schools), football played according to the Association Rules
ah, so I see we are slowly coming back to my original suggestion (OP) re Italian ((ooni...) socker (football) fan :)