I'm not sure that Corbyn's honesty is not appreciated by the public, I think people want trustworthiness every bit as much as dogma.
I don't even think it was charm, charisma or dogma from the Leave campaign which swayed the voters in the referendum. I believe it was the false assurances about the NHS and immigration, especially immigration.
Immigration is the elephant in the room and any party wanting the working class on their side has to address it. There is a difference between racism and xenophobia and the fears of some people are understandable in an economy relying on cheap Eastern European labour. The people are not wrong - this happens because our government allows zero hours contracts, turns a blind eye to 14 hour days, favours short term temporary contracts, forces the sale of social housing etc etc etc.
This has been a long time brewing and it is no coincidence that parts of the north where the coal and steel industries have been decimated without any viable alternative employment put in place voted against the government on something many of them see as primarily an immigration problem.
None of this is the fault of the actual immigrants, or of Corbyn or his supporters. Cameron, Blair and Thatcher have been responsible for destroying workers' lives. But, it needs to be talked about openly and honestly and real solutions for real people need to be found.