Nick, well done on the crossing.

Being over on that side of the pond you'll be looking for a Waeco/ Adler Barbour Cold Machine. It uses the Danfoss compressor. For your installation I'd be looking for the air cooled version which has a Danfoss BD50F compressor.
You build your own insulated box, insulation being the key to success, and then fit the compressor in some convenient place within 15' of the box.
The evaporator, basically an alloy open ended box in which you keep the ice cube trays and anything you need to keep particularly cold, is fixed inside the box and provides the cooling.
The two componants are connected by the refrigerant cooling lines which have a clever sealing system so the gas doesn't escape when you connect and disconnect during installation. A simple thermostat tells the compressor when to run and when to switch off.
These systems take up to 5 amps when running; the success of your insulation, size of box, ambient temp etc will determine how many hours a day it runs. Reckon in 50% running time in the Tropics.

All the bits for a fridge can be had second hand in Florida, at such places as Sailorman in Ft Lauderdale - just look for 'Cold Machine'; you can buy new from West Marine, Defender etc.

An alternate system is to buy a complete 12v fridge, such as the Norcold - which you can also pick up second-hand. They make installation very easy - no box to build - and they work very well. We had one on Adriana for three years in the Caribbean.
Power consumption for the Norcold on Adriana was around 60 - 100 amps per day. This is about the same as for the Cold Machine on our 41' ketch, also in the Caribbean.