(continued) . . .
I think that you're going to have to rely on using throws but, as I've said, you might well spend less time straightening these than you would on straightening expensive sofa covers. (The last set of sofa covers my parents bought from Plumbs were made to measure and we still had to keep straightening them!). I suggest heading for a 'cheapo' shop and buying several throws. If you've got lots of throws on a single sofa, it won't show if they move around a bit, so you won't have to keep straightening them. (I bought a couple of pairs of lined curtains, at �9.99 each, on Wednesday from just such a shop. They were next to the throws, which, I happened to notice, were all within the �5 - �10 range. So, at those sort of prices you could probably buy quite a few throws without breaking the bank).
I'm sorry that this post doesn't directly answer your question. I hope that someone will post another answer to say that I'm spouting a load of rubbish and that they can point you towards a source of well-fitting cheap sofa covers. I fear, however, that you might have to live with the throws.
Chris