Her to you: if your number is already in her phone contacts as +447something then no change; if your number is in her phone contacts as 07something then she may need to change it to +447something. Maybe not in Ireland, I'm not sure.
You only need to put a country code in if the number you are calling "lives" in another country (not just visiting) - Mrs B's mobile "lives" in the UK so doesn't need a country code so long as the phone calling it "lives" in the UK, as yours does.