The problem for Starmer here is that his appeal that he is honest and has integrity by offering to resign if the police find him guilty has 2 large holes in it.
1. The Labour Party has already been caught out lying about BeerGate. They lied about who was in attendance, first Angela Rayner wasn't there then it turns out she was. They also lied about it being "spontaneous" when it was in the official diary with the plan on who was ordering the curry.
Pretty sure the 'spontaneous' part originally came from James Cleverley, not anyone at Labour. Though I can stand corrected. The Rayner thing seems to be more a misunderstanding rather than an attempt to conceal anything.
Of course the public probably think both are lies so.