Obviously (as noted elsewhere) this depends on what you understand as "cheddar", and is likely to lead to snorts of derision from most Brits; however, although colourings are not added to high-quality English cheddar cheese (or as far as I know to the New Zealand or Canadian varieties which dominated the British market before the UK entered the EU in 1973; during that period, when British food did its best to fulfil its reputation for appalling blandness, acidic Canadian cheddar was one of the few things that actually tasted of anything. But I digress.) there is in fact a fairly healthy traditional market for red cheddar in north-eastern England (roughly speaking, east of the Pennines and north of the Trent); this is mild creamery-produced stuff of no particular merit.
However, other traditional English cheeses of better repute are coloured orange (the dye of choice being carrot juice or industrially extracted beta-carotene which also incidentally goes under the name of vitamin A; as far as I know annatto is only used in industrial-scale production) to varying degrees. These include:
- Red Leicester - a mild cheese, not vastly dissimilar from cheddar, good for toasting. Virulently orange.
- Cheshire - comes in both red (a milder pink in fact) and white variants, a crumbly acidic and fresh-tasting cheese.
- Shropshire blue - a fairly firm blue cheese, milder and much less astringent than Stilton; oddly, one of the few British cheeses which has been successfully marketed elsewhere in Europe. Also comes in a white variety but the orange one is more common.
The northern French hard cheese mimolette is also annatto-dyed, supposedly to distinguish it from Edam of which it was a copy, albeit one which is somewhat better than current versions of the original.
An orange processed cheese supposedly originating in the UK (and I believe manufactured by Kraft) which appears to be similar to American cheddar (which I've never tasted) is marketed in Belgium under the name "Chester"; its availability here supposedly dates back to the stuff brought over for the British troops on the Western Front in World War I, but I doubt that they actually had anything quite that plasticky.
It should be noted that the British have been very slow and late getting into the controlled labelling of origin thing, so very few of the names offer any particular guarantee of authenticity; cheddar in particular has been officially decreed to be a generic term usable by producers anywhere.