Let's keep this straight: there are BrE speakers who erroneously say could care less as well. But AmE speakers do it a LOT more often.
Besides could care less, the use of adjective forms in adverbial slots is, from time to time, brought to me (by BrE speakers) as a certain sign of AmE inferiority and of the degradation of BrE through the influence of AmE. Here are some examples, in case you don't know your adverb from your elbow:
He did it realADJ well. VERSUS He did it reallyADV well.
He did it realADJ goodADJ. VERSUS He did it reallyADV wellADV.
She did that so cuteADJ. VERSUS She did that so cutelyADV.
When BrE speakers chide me about "ignorant" aspects of AmE, I have a ready arsenal of BrE illogicalities, "errors" and losses to throw back at them--some of which have been or will be discussed here. And the adjective-as-adverb issue is easier to dismiss as "not our fault", since using adjectives as adverbs is an established feature of several BrE dialects (such as this one from Yorkshire). Furthermore, both adjective-as-adverb and could care less are considered to be "non-standard" in AmE--we do have some standards, I say. But on the way home from an American Christmas party, I remarked to Better Half "I don't think I've ever gone for so long without hearing an adverb," to which non-linguist BH replied, "I wouldn't have been able to say it that way, but I know what you mean!" (The last adverbless example above is an actual example from the evening.) One does hear adjective-as-adverb in BrE--and not just in noticeably dialectal speech. But it's certainly not heard in BrE at the rate one hears it in AmE speech these days.
Tomorrow we're back to Blighty, so this ends my (BrE) holiday-/(AmE) vacation-time blog-o-rama. Next week we'll be back to term-time posting frequency.