Yes, it would more than likely be covered by TUPE. You should be able to find more info on the ACAS site Molly...too knackered to explain myself but, in a nutshell, it's the law covering what happens to employees in the transfer of a business.
It's to protect them from all just being got rid of but there are circumstances in which people can be let go.
Also, at the end of the day, the law is all well and good but the other employment laws and practicalities of taking any action if anything was done wrong also need to be considered.