A simple search of the Venezuelan Embassy in United Kingdom webisite states that if entering by land or sea you need to apply for a tourist visa prior to entry. It seems the airlines are allowed to issue on the spot visas. I would guess you would need to plan out which country to apply for the visa at the respective Venezuelan consulate. I would confirm beforehand that the Venezuelan consulate in the country issues the visa to UKers.
You should also call the VZ embassy in UK to get the latest and more accurate info.
NZ seems to be the same.
Do I get a  now?
Check it out= http://venezuela.embassyhomepage.com..._london_uk.htm
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