Councillors in Patrick Mercer's constituency of Newark, where he has a 16,000 majority, have expressed their shock at the news of his resignation.
Councillor Peter Duncan said he always thought of Mr Mercer as "a very solid citizen".
He added: "If this news is true then I am shocked. I thought he was a very strong individual with a strong point of view. He will be missed."
Another Tory councillor Derek Evans said: "I'm very surprised at the news. I've a lot of trust and faith in Patrick. I have utter faith in him as an MP."