Gas and electric fridges
The usual solution, and possible to pick up electric fridges second hand - but gas fridges use lots of gas, and electric fridges use LOTS of electricity. A much better way would be to find alternative ways of keeping your food (and beer) cool.
Storing stuff in the canal/river
An obvious way to keep things cool is to chuck them in the canal/river. Obviously you need to keep hold of them somehow so they don't just sink to the bottom! If you have old tyres hanging off the side of your boat as fenders you can put things inside them. Otherwise a bag with a piece of string might do the job.
An obvious concern, particularly on canals, would be the yuck factor of what's in the water coming into contact with your food (or the neck of your beer bottle!). What are good things to put your stuff in before chucking them overboard?
Using the bottom of your boat/bilges
Some people have suggested storing things directly on the bottom of your boat, so that the cool water under your boat can help cool your stuff.
In houses you can make a cupboard with vents at the bottom and a tall chimney, painted black at the top. This causes a draught from the cooler floor level to go through the cool box and up the chimney. Obviously this wouldn't work so well with boats where even the floor level can get quite hot in summer. Perhaps this could be combined with drawing air from your bilges, which are cooled by the water under the boat?