There are many lists of words that are British English translations for American English. These amateur lists are often flawed. One of the most commonly repeated errors, in these lists, is the claim that desiccated is American English for shredded. Desiccated is a high register synonym (see article High-Register Synonyms) for dried. Shredded means: ripped into small pieces. These words do not mean the same thing!
The usual example is dried shredded coconut. So I did a quick check on the frequency of use. The UK uses the term desiccated coconut over shredded coconut at a rate of 1 to 1.6. (According to the British National Corpus) The US uses shredded coconut over desiccated coconut at a rate of 1 to 2. (According to the Corpus of Contemporary American English) Not only do both sides of the Atlantic use both words, but the US uses the supposedly UK word more often.
The word desiccated was borrowed from Latin in the 16th century, during the Early Modern English period because it sounded fancier than saying dried. English borrowed many words from Latin at that time. The words shredded and dried are both from Old English.
These words are used on both sides of the Atlantic. I suspect that these words originally got added to the list by a less educated British English speaker who was simply unfamiliar with the word desiccated.