Get the orange campo viejo if it's a tenner budget.
Otherwise raise said budget and buy yourself a decent Burgundy (matches your preference from what I see here): £15-30 should be adequate.
Otherwise I'd have a look at acquiring some second label bordeaux or cheap(er) Pomerol. [Edit: which sadly won't be available in most supermarkets, however for £45 alter ego de Palmer is a bargain; strongly recommend it at this price]
In fact £30ish can get a delicious Pomerol. [Edit: unlikely to find any in a supermarket frankly]
Ok so I know I've suggested a bit above your remit, but it really is worth it. And, can you really put a price on pleasure? You'll enjoy it a lot.
However, RE: non-sulphite Sainsbury's Shiraz etc. I'd personally buy that if there were no others on the aisle that you think you could drink (for instance in my local one the Organics are probably the best bet for £6 and I have to say that they aren't all that bad at all!)
You could I guess get one of those Devil wine reserves... Casillero del Diablo or something I think they're called. If its under £8 have a go with that. Not ideal mind.
Otherwise, if I had £10 to spend, I would go with the Orange Label Rioja (presumably you're going to a supermarket) or see what the French selection is like (don't know but if your local is like mine, then it's poor).
I agree with the comment regarding wine on offer. Lussac is sassy to say the least. Avoid. However, if you want to get bashed for £7 (used to be 3 for £10 mind) get some
