Regarding Jeff, anyone who drinks a lot, do you reckon

I'd say both, given his characterisation and what we know about him in the film.

Heavy drinking was very much part of the London underworld culture at the time and nearly every character in the film are never too far away from the bottle. Early on Harold's boat Victoria tells him to lay off the booze, which he ignores this by topping up what appears to be his Bloody Mary with vodka. And I'm assuming this is still late morning/early afternoon. Geoff's drinking almost certainly helps him keep his nerve throughout the caper, but I think he would be knocking it back anyway in keeping with the standard behaviour of his chosen profession. Only one character, Councillor Harris, is acknowledged as having a real drinking problem, but that is probably because he can't be trusted to keep his mouth shut when under the influence.