Thanks very much, peeps. That is somewhat disappointing but at least that's one avenue ruled out, if he's definitely with Mary Ann in 1901 and 1911. (I have now found some Electoral Roll entries via Family Search for Albert Edward Collings at Lower Charles St - no longer there, but near Meredith St in Islingon, 19010-12 - renting a single room, no mention of a wife??; but there's also an Alfred Edward Collins also on electoral roll at Florence St, Depford (and another at Newington Causeway). I don't know. I give up there. I suppose the names were fairly common.)
Back to the matter in hand. Yes, there's definitely some kind of story behind this. The details on Albert's 3rd son Cecil are somewhat odd too:
https://www.dropbox.com/s/q7rzg92pgyj59sn/Cock-Collins%2C%20Cecil%20-%20birth%20cert.%201904-07-20.pdf?dl=0 The parents were apparently temporarily in London. (I haven't found any passenger records of their transit, and presumably they would have had two other infants with them?!). As you can see, the mother's address is given as 146 Caistor Park Road, and the baby born at 20 Corporation St, about half a mile away. It's all most peculiar. They were back in Cape Town by 1907 at the latest, when the 4th son was born.
Annette - that service record in the Bechuanaland Police does sound promising, seeing that he is named variously as Constable, Sergeant and Police Inspector on various sons' birth certificate. I will digest this information and work out how to go about getting a birth certificate for the Truro Cock. (Is it worth my posting requests for further information in the Cornwall forum, do you think?)
Another interesting thing to note is that Cecil is given the 3rd name Hopecook (which I think is a misspelled version of Hopecock, which I came across somewhere else along the way) - but on all later documentation I have, inlcuding his death certificate, his 3rd name was Christopher, by the age of 23. However, the header information given on this site here:
http://www.ancestor.co.za/COCK-COLLINS, which refers to his death, says "CECIL SIDNEY CHRISTOPHER COCK-COLLINS ALSO KNOWN AS CECIL SIDNEY HOPECOCK COLLINS 1952".