Struggling to find any information on the origins of this expression. Is it just a form of the more specific "knocking on 60" meaning you're knocking at the metaphorical door of 60?
Eric Partridge & Paul Beale, A Dictionary of Slang and Unconventional English, eighth edition (1984) has this relevant entry:
knocking on (a bit). Growing middle-aged—or elderly; or merely being older than the speaker: low coll[oquial]: since ca. 1930.
This entry is by Paul Beale, indicating that it was added in the eighth edition. The fifth edition of Partridge's dictionary (1961) has no entry for "knocking on." None of the other fairly recent British slang dictionaries I consulted (including various books by Green, Ayto's Oxford, Ayto & Simpson's Oxford, and Thorne) have anything for "knocking on a bit" or "knocking on."
Oddly enough, the earliest mentions of "knocking on a bit" that appear in the British Newspaper Archive involve motorists and the phrase seems to have meant "speeding." From "Motor Scout Who Did Not Salute," in the Leeds Mercury (May 16, 1928):
"I'm glad you understood why I did not salute, because you were knocking on a bit. Please go slowly through the next village...I did so and kept my eyes open. Standing by the end of a lane and trying yo look very unobtrusive about it was a man who was obviously policeman in plain clothes.
And from "Speeding" in the Lancaster Guardian September 17, 1937):
Eric H. Giles, of Blackpool, was fined and had his license endorsed for exceeding the speed limit with a public service vehicle. P.C. Williams said that defendant's speed at Yealand Redmayne was over 41 m.p.h., and said that when stopped defendant admitted "I know I was knocking on a bit, but it is the first time for four years." He was driving a party by motor-coach to Gretna Green.
A similar idiomatic expression in U.S. English is "pushing 70 [or some other number]"—wording that may be applied equally to traveling speed (where it means "nearing 70 miles per hour") and to age (where it means "nearing 70 years old"). I don't know whether the British expression "knocking on a bit" began as a slang term for vehicle speed and evolved into an expression about age, or whether the expressions arose separately, but it's tempting to imagine a connection between them.
The more common expression appears to be knocking on a bit which, according to the Short Slang Dictionary by Paul Beale and Eric Partridge, has been used from the 1930s. Though evidence from Ngram suggests that the expression is from the '60s.
Note that knock in that sense can be used without the preposition:
- informal with object Approach (a specified age) ‘he's younger than his brother—knocking seventy’
I think it refers to knock meaning hit something producing a sound, probably on the idea of having reached a point which is an entrance to a further point.