All the TV chefs say "If it isn't good enough to drink, it isn't good enough to cook with", so they (and I) would not recommend necessarily looking for the very cheapest wines.
If you're cooking with red wine, look for something 'full-bodied'. I'd suggest looking for the word 'Shiraz' on the label. It's a grape which always provides plenty of fruity flavour and it's almost impossible to buy a poor quality Shiraz. (i.e. any bottle of Shiraz should be good enough to cook with will give great flavour to your food).
Alternatively, for a full-bodied red, forget about the grape and look out for the countries. Almost any red wine imported from Eastern Europe (particularly Hungary) tends to lean towards the 'full-bodied' end of the scale (and the quality is easily good enough to cook with). Much the same can be said for many of the cheaper red wines from Chile and Argentina.
When it comes to white wines, the best results are probably obtained by using fairly dry wines but still with some 'fruit' in the flavour. A good (cheap) grape to look for might be Sauvignon Blanc. Alternatively, just check that the wine is labelled 'dry'. Italy produces some of the best cheap dry white wines and the vast majority of Italian whites sold in this country are of a reasonable quality (and certainly good enough to cook with).
Chris