The former defence secretary, who was sacked over a leak of National Security Council talks on Huawei, said the talks were “destined to fail”.
Writing in the Mail on Sunday, he said: “Even if Labour do a deal, break bread with the prime minister and announce that both parties have reached an agreement, it can only ever end in tears.
“The Labour Party does not exist to help the Conservative Party. Jeremy Corbyn will do all he can to divide, disrupt and frustrate the Conservatives in the hope of bringing down the government.
“His goal, and he has made no secret of it, is to bring about a general election.”
Mr Williamson, the Tory MP for South Staffordshire, said the prime minister seemed oblivious to the fact many Tories believe she is “negotiating with the enemy”.
The former cabinet minister said there was a simple calculation that a deal could pass with the combined votes of Labour and Conservative MPs, but “tough realities” must be faced if the deal was “far removed” from expectations.
Mr Williamson said this could mean Ms May has support from less than half of her MPs, including ministers.
That would lead to “knife-edge votes” and yet more defeats for for the PM thanks to Labour rebels who want another referendum, he said, alongside SNP, Lib Dem and Change UK MPs who have pledged to vote against.
Changes to the Labour-Tory deal if it did not meet expectations could allow Mr Corbyn’s party “to credibly say it is not what was originally agreed”, he added. ”This is when Labour will finally kill it. It is politically naive to go down this route.”
Mr Williamson warned the prime minister she was turning her own supporters against her, and suggested new leadership was needed.
It came as polls suggested the Conservatives had fallen more than a dozen points behind Nigel Farage’s Brexit Party in the European parliament election runnings – news which itself followed a bruising performance in local council ballots earlier in May.
On Saturday Ms May was filmed playing football with children in her Maidenhead constituency.
Additional reporting by PA
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies