'Official'-type answer:
A 'best before' date indicates that the quality of a product might deteriorate after that date, but consuming it will present no risk to health. (It's perfectly legal to sell foodstuffs after their 'best before' date, as long as there's no pretence that the product is still 'in date').
A 'use by' date indicates that there's a potential risk to health if the product is consumed after that date. (It's illegal for a shop keeper to even give a product away, to a member of his staff, after that date). So you shouldn't eat your cheese.
My totally unofficial, 'don't-blame-me-when-you're-writhing-on-the-f
loor-in-agony'
answer:
The bacteria in cheese generally only present a risk to those with deficient immune systems (e.g. young children, the foetuses of pregnant women, the very elderly and those with HIV or other medical conditions impairing the human immune system). If it looks and smells OK, I'd have no hesitation in eating it. (Indeed, I'd go further and ask why you ever put it in the fridge in the first place? Cheese should be allowed to mature at room temperature).
Chris