Seem to have lost a post so I'll try again.
Robert Service attribution seems highly unlikely to me. The piece(or at least the versions I have heard) seems to me a knowing slightly ironic 2oth century parody of Robert Service.
   I've seen it attributed to Noel Coward, A.P. Herbert and possibly others as well, on what evidence I havent a clue. But that sort of genre of writer seems a lot more likely than an actual bit of Robert Service. Take a couple of quotes:

He twitched his arsehole in and out
And made his balls inflate
Until they looked like granite knobs
Atop a garden gate

Now Dead-Eye Dick and Mexico Pete
Had been panning up Shit Creek
And they'd had no luck by way of a fuck
In well nigh on a week

Does that sound like Robert Service? I think it sounds like a devastating parody of the style.