The former Tory deputy chairman announced he was switching parties despite being close to agreeing a comeback after the whip was withdrawn.
Mr Anderson declared "all I want is my country back" as he stood alongside Reform leader Richard Tice in a hastily arranged press conference.
A senior Tory source said: "He has been signalling to us he wanted to come back. I don't know where his head is at. It's disappointing.
"He was trying to make an important underlying point but it was made quite crassly. It could have been dealt with.
"He was signalling that he was open to an apology. MPs are furious about it.
"They are upset by the disloyalty.
People feel let down." The Ashfield MP had accused the Conservatives of stifling "free speech" after he was suspended for speaking his mind about London mayor Sadiq Khan.
Mr Anderson met Tory Chief Whip Simon Hart last Monday for talks about how he could return to the fold.
The pair were due to hold more discussions to pave the way for him to be given the whip back.
Conservative deputy chairman James Daly said he did not understand Mr Anderson's explanation for quitting.
"For me this is a really, really sad day," he added.
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