Quite possible. And for the cases Nigel gives, I'd agree. But "Not much cop" isn't what you'd expect from them. I'd have expected "Not worth copping" or something like that. I'd not be surprised it's got some other source.

"Cop" itself is on any case an odd word - it's been suggested that it's cognate with "capture", and that cop or copper also comes from that - but the vowel change from "a" to "o" isn't what you'd expect.

I'm wondering whether there might not be a Shelta or Romany origin.