During that time Churchill was treated as a pariah, shouted down/heckled at universities when he tried to give speeches, and mostly ignored in Parliament and by the people in power at the time. Chamberlain was one of those people.
And chamberlain included Churchill in his war cabinet - and then when Churchill became prime minister he included chamberlain in his war cabinet as Lord President of the Council where Neville ran the group in churchill’s absence. A mixed and famously unfortunate history but chamberlain’s citizenship and loyalty to UK was not a matter of serious question. ( later Churchill critiqued chamberlain for, as you said, having been one of those who failed to, or who were opposed to, preparing for the war ).
“You were given the choice between war and dishonor. You chose dishonor and you will have war.” - Churchill to Chamberlain after Munich.