Tropical in origin, but are grown very successfully in temperate climates with a long warm summer. They are grown in Spain and Italy, and grow well even in northern parts such as Catalunya and Veneto. They were a staple for the Maori of New Zealand. In the US they are cultivated commercially in Kentucky, Tennessee, and North Carolina (the main producer), as well as the gulf coast states.

So we aren't too many hundred of miles north of good growing areas. But basically the problem in Britain is that the growing season normally just isn't warm for long enough for outdoor growing to have much chance of success. Better chance in a greenhouse.

The history of the plants is very interesting. They were cultivated from about 2500BC in central and southern America, and from about 700-1000AD in the Pacific Islands, including New Zealand. It was also grown in highland New Guinea before European contact, though possibly from more recent times. But the Philippines knew it not before European contact. The name for them is more or less the same - kumara or some variant - in Quechua (main Peruvian language), Nahuatl (main Mexican language) and Polynesian languages (including Maori), who all cultivated it before European contact. So there is some quite strong indication of Polynesian - South American contact. Although there is some very rare native sweet potato in Polynesia, it is not the same species as South America, and the Polynesians cultivated the South American version, via cuttings.

The Maori trained seagulls to pick bugs off the leaves, would you believe it.