When TB goes the Labour Party must hold a leadership election. TB cannot simply hand over to GB.
The Labour Party electoral college gives equal votes to the parliamentary Labour Party (PLP), the Trade Unions and the constituency parties (CLP).
TB & GB control the parliamentary party. No-one can control the CLPs. To secure their plan TB and GB must therefore ensure the support of the Trade Unions.
Ergo, cabinet ministers have begun wooing the TU Leadership. I doubt if its beer and cigarettes at meetings these days though. More like fine wines and caviar. It might also be wise to check out the waitresses...