The problem in these sorts of situations is that
everybody in the WORLD has some sort of exigency or pretext for which their prior immigration history should be overlooked. There was a thread this morning about the legacy book, and part of the reason there's still half a million cases is related to the situation in this thread.
In a case like this, it would be reasonable for an IO to see a letter from your bf's GP explaining why you should be admitted. Or your bf's vicar, or etc etc etc.
Generally your case is better handled by getting an entry clearance which has been assembled and blessed by a top-notch solicitor. Mariano Soloman is arguably the best choice based upon what you wrote.
But overall, there is nothing to prevent you for applying at a UK port for LLE (or even TA for that matter). You might get bounced, or you might not. Nothing at all prevents you from trying.