Sweet potatoes are basically a tropical veg, which means they LOVE heat, which is also why they're drought tolerant. In commercial fields they lay sheets of plastic weed barrier for exactly that purpose as they're planting thousands of acres of sweet potatoes and haven't time to weed. The plastic also holds in the ridges they build for maximum soil depth and good drainage.
The potatoes themselves need heat to grow but they won't tolerate being cooked so the vining top growth is allowed to ramble on top to shade the soil while gaining maximum sunlight on all leaves. (not sure this 'problem' exists in the UK
) To wigwam them means there'll be some shading and a resulting diminish in cropping. Plus, the leaves just plain don't like to be trained up objects as you can do with melons, cukes and such. There's a main growth 'stalk' if you will, below ground from which the tubers sprout widely and with fertile loose soil, the crop can be large as well as huge sizewise. The vines themselves don't root unless severed somehow and the leaves with stems touch soil. You can get new plants from this method but by now there's likely to be insect damage, maybe some fungal damage which you don't want to propagate so its best to take new shoots from freshly sprouted tubers. So basically, you don't want to wigwam or allow the leaves to climb because you'd be stepping on the crop without realizing it as the underground spread can sometimes be wide if you have any hardpan. Is this what you wanted to know?
Here's a link to pix for starting your own slips. Store bought sp's might have a growth stopper sprayed on them as mine did and though I started mine last year in early March they were ready for planting out in July which was too late. So I kept the tuber going as they can keep putting out slips for up to 5 years.
http://grandbobsgarden.blogspot.com/2009/05/how-to-grow-beautiful-sweet-potato-vine.html