UK passport - Hanoi>Beijing for 3days>London (via Dubai)

I am a UK passport holder. in November I will travel from Hanoi to Beijing Capital Airport with Vietnam Airlines. I will stay in Beijing for 3 days and depart from Beijing Capital with Emirates to UK via Dubai.
My travel Agent (Affordable Luxury Travel) says i must have a visa, as the term 'transit' is when the itinerary is on one airline. I don't believe this is correct. Do you have to use same airline to arrive in China and leave China?