u aren't married, so i wouldn't worry too much about it, engagements prob' mean jack shit in the courts, it's marriage that counts,
there's a bit of a myth in the UK that if u have a "living together" relationship that lasts a over certain length of time, your partner would then become your "common law" wife (marriage or not) and then be able to claim half of whats yours , but i believe this to be false,
i reckon for your partner to make any kind of a claim against your business/profits etc, she would have to prove she contributed a significant amount into the business, both phsically and financially,
i get the impression she did neither,
don't let her lawyers scare you, keep any letters they send u, YOUR lawyers will want to see them, if they are wrong in telling u to shut down your business, u can sue the shit out of them.

good luck matey.