I listened to Adam McNaughtan sing THE GLASGOW COUNCILLOR on Spotify. The version I heard there was from a various-artists album "Glasgow Horizons" (1990). There is one whole additional verse (compared to the one Susanne posted):

3.5 Ah'm mair working class than whit you are.
Ah've credentials that just cannae fail.
When Ah'm oot on the bevy, Ah always drink heavy
And nane o yer yuppie real ale.
I'll admit that I'm ...
And ... case,
But it's ...
Cos ma heart's still in the right place.

Also, verse 4 line 3 is different:

"Cos Ah always feel in agreement wi' Neil"

I suppose that would be Neil Kinnock, which would mean this is an older version than the one above. Wikipedia says Neil Kinnock was head of the Labour Party 1983-1992.