Bitter, Best Bitter, Extra Special Bitter—these denote beers made in the style of English Pale Ales. This is an intense, salty yet smooth cheese and it really likes to match with a full-bodied ale with lightly fruity and caramel notes. This is an intense, concentrated cheddar that shines when paired with a complex beer.
Some sweetness is nice, to counter the salt. This calls for something British (or British-styled). Beers in this family bring varying levels of malt, hops and creaminess. This means extra fun for you as you experiment.