Aren parking attendants / traffic wardens supposed to give a few minutes grace before issuing a ticket?
No. You are only allowed to stop to load or unload goods or set down a passenger (other than on zig-zag lines and on red routes where a single red line usually bans stopping and parking during controlled hours and two red lines bans stopping and parking at any time). If loading or unloading then you must be able to prove as such.