Boris Johnson won a no-confidence vote on Monday by 211 to 148.
Sir Graham Brady, chair of the Conservative 1922 Committee, said 359 votes were cast. There were no spoilt ballots.
Ahead of the vote, Mr Warman tweeted that constituents had told him to act “in the national interest” and vote against the motion of ‘no confidence’..
He said that :the constituents who gave him guidance included supporters and non supporters of Mr Johnson.
"”I’ve always been clear that some of what went on at Downing Street over lockdown was deeply wrong.
"It can’t be wiped away by Brexit, or the success of the vaccine programme or the UK’s role against Putin.
"but the Prime Minister has apoiogised and those examples, with others, do show what Boris Johnspn’s government can achieve when it is bold and ambitious.
"Those qualities are why he was entrusted with a Conservative majority that give a real opportunity to deliver for British people.
"So rather than leadership contests and votes of confidence, I want to see the government deliver on the issues that fill up my inbox – the cost of living, infastructure, childcare and a host of other matters.
"It is so we can get on with doing that in the national interest.”
Horncastle and Louth MP Victoria Atkins, who serves the Spilsby area, also voted against the no-confidence motion.
Deputy prime minister Dominic Raab told the BBC Boris Johnson has has "redoubled in his commitment and focus" on the government's agenda.