Swapping visa question

wondered if someone would be able to help me out with info on UK visas. My sister has been in the UK for the last two years on a tier 5 visa which expires on the 15th of Feb. She's been back in New Zealand applying for a tier 2 visa which commences on the 1st of Feb. She's trying to get back to work as a teacher asap but no one at the immigration office will tell her whether she's allowed to enter the country on in January on her old visa before the new one takes over?

Would be incredibly appreciative of any help!