on my doug - Rhyming slang.

[198x]

Years ago when I was at school if you were on your own you were said to be "on your doug" or "on your douglas"

Now I heard 'on your Jack' earlier and it made me wonder where did "doug / douglas" come from? I haven't seen it on any rhyming dictionaries and yet a load of people I know of say it.

[Quizmonster]

Well, the phrase, 'on your tod' refers to an American called James Todhunter Sloan and in Australia, 'on your pat' apparently refers to an Irish immigrant called Pat Malone. You'll see that, in both cases, the actual surname rhymes with 'alone' or 'on your own'. Really, therefore, both are examples of rhyming slang.
I imagine, thererfore, that the 'doug' example referred to someone called Doug Jones or some such surname that also roughly rhymed with 'alone'.

[heathfield]

In support of QM, the phrase 'on your Jack Jones' was commonly used in the armed forces.