Keith Barrow attended Mr Farage's rally in Birmingham on Saturday, and said he expected his new Brexit Party to take a huge number of votes from the established parties.
He said he had not yet decided how he would vote in next month's European elections, but said it would definitely not be for the Conservatives.
Mr Barrow, who is still an active Conservative Party member, said Mrs May needed to go quickly if the Tories were not to be wiped out at the poll.
"I went to the Brexit Party rally, to be honest just because I was curious, I think many people are," he said.
"I have not made my mind up how I will be voting, but I'm certain I won't be voting Conservative. I think it's an absolute disgrace we are having European elections at all."
Mr Barrow, who led Shropshire Council from its formation in 2009 until 2015, said it was hugely important that MPs honoured the result of the referendum.
"It's what people voted for, 75 per cent of parliamentary constituencies voted to leave, but it seems we have a majority of Remain MPs.
"We were told it was a once-in-a-lifetime opportunity, and that they would deliver whatever we voted for."
He said he saw no way out of the deadlock until Theresa May resigned, saying she had handled the matter badly from the beginning.
"She should have gone after the General Election, it was totally unnecessary, and we lost because there were manifesto commitments that most MPs were not even aware of.
He praised North Shropshire MP Owen Paterson for sticking to his guns in demanding a clean break from the EU, but believed Mrs May's inner circle were out of touch with the mood of the country.
"I don't think Theresa May and her colleagues understand the anger out there in the constituencies," he said.
"She said no deal was better than a bad deal, but she has come with something that nearly everyone, leave or remain, thinks is a bad deal.
"It is the worst of both worlds, it will leave us forever locked into rules we have no say over, if that goes through it would be better we never had the referendum at all."
Mr Barrow said he believed new smaller parties such as the Brexit Party could spell the end of the two-party system.
"The established parties have no idea what they have unleashed," he said.
"The EU elections will be the start, I’d be very worried about parliamentary elections if I were a sitting MP. How many grassroot supporters will stay to help?"