Cheap Food in the EU?

In the middle of a reasonably well constructed argument in favour of the EU I came across this wonderful piece of fiction

If UK were not a member of the EU, then of course it would have to pay higher prices for food products imported from the EU than the UK does presently, because the rest of the EU would still be subsidizing the French farmers, who get EU subsidies to produce food for all us. The Member States would then not foot the subsidy bill and give the UK a free ride. Of course, the UK could then subsidize their own farmers, also costly, or import more food from elsewhere overseas, and rely on those markets, which might ultimately also turn out to be costly.

This is the best distortion of the CAP I have ever seen. Even Pro-EU bloggers like Lose the Delusion and Europhobia are critical of the CAP. Here however is an opinion that could have come out of an official EU document. If the member states are unwilling to foot the bill to subsidise someone else’s food, where does that leave the current Export Subsidies that aid organisations criticise so much? What we would actually see is freedom to import from the most productive farmers in the world or buy the cheapest products from poor countries. Our food bills would go down not up.