Can you have a business transfer involving only one person?

Yes, as long as that one person can be said to amount to a separate “economic entity”. In the leading case, Schmidt v Spar-und Leihkasse Der Früheren Ämter Bordesholn, Kiel Cronshagen: C-392/92 [1994] IRLR 302, a single cleaner was engaged to clean one branch of a bank. The ECJ ruled that her employment transferred under the Acquired Rights Directive when her employer replaced her with the cleaning agency that was already responsible for cleaning the bank’s other branches.