OP, I think you're getting a rough deal from people who don't understand cultural difference or bilingualism.
That said, your DC is 3/4 British by the sounds of it, and living in the UK. You do need to think about preparing her (I think you referred to DC as her in your OP) for the UK school system.
My DS referred to others as Mummies and Daddies too. For him it meant woman/lady and man. This continued until he was 4 or 5 and he only speaks one language.
He also couldn't grasp that within the day we had morning and afternoon, he always just said morning or night.
DS has additional needs (Asperger's) and actually has a very large vocabulary, but when he was little he did get his words mixed up a lot, especially what would be seen as simple words, because he was too busy focusing on bigger words.
As your DC is learning 2 languages, I'm guessing she mimics her peers when she is unsure of the word to use which has led to calling your bf Daddy, and friends parents mummy and daddy etc. This has probably led to her thinking the same way as my DS and equating these words with lady and man.
I do know two people that always referred to their DFs by their first names, people always thought they were stepdads. I also know someone that got together with her DH when her DD was 1. DD referred to her stepdad as Daddy and her bio Dad as Daddy Pete*. Bio Dad wasn't really massively invested in her, so he didnt kick up a fuss. However, I also believe a daddy is the person who raises a child, blood counts for nothing if they're not around (and you say ex has not been around for much of her 3 years?)
But your DD needs to start to understand British naming conventions if she will go to a British school. It may not have worked so far, but you must be consistent, and everyond must support you.