We do not know that Battersea did not try to or even actually make contact with PB. We know that he did not make contact with Battersea. The AAIB report will say if Battersea made any transmissions, and (hopefully) what radio frequency PB had selected.
Typically, though, on being passed to another frequency I have to change my set and make the opening call. The new handler will wait for me, else how does he know I have changed my frequency?