Potatoes start from seed potatoes, not from plug plants. Seed potatoes are special potatoes grown specifically to grow for a crop rather than eat. It's pretty late now to plant seed potatoes but if you can find any, not much to lose by trying, they're not hugely expensive and are likely to be reduced by now. Places to try Wilko's, B&Q, Homebase, Woolworths, Pound shops etc are usually cheaper than garden centres. You won't get much choice of variety at this stage so just take what you can get, but make sure they haven't gone soft and shrunken. If they have shoots (chits) on that's OK.
Earthing up is done when the plants reach around 8". You draw the soil up from the sides of the plant to cover most of the leaves. This encourages more tubers to form and it excludes light from the developing potatoes so you don't get green potatoes.
Can't help with your clay soil, I'm on free-draining sandy loam where the challenge is to hold onto moisture!
