That is eight short of the number needed to trigger a party leadership contest, the mechanism through which May could be forced from office and replaced by another Conservative.
May has been struggling to maintain control of her party since a snap election on June 8 in which she assumed she would win by a wide margin but instead resulted in her losing her parliamentary majority.
Divided over how to extricate Britain from the European Union and hit by scandals involving ministers, May's government has failed to assert control over a chaotic political situation that is weakening London's hand in Brexit talks. An earlier bid to unseat May in the wake of her disastrous speech at the annual party conference fizzled out, but many Conservatives remain unhappy with the prime minister's performance and talk of a leadership contest has not gone away.
May has lost two cabinet ministers in as many weeks: Michael Fallon quit as defense secretary after getting implicated in a scandal about sexual misconduct in parliament, while Priti Patel resigned as aid minister after she was found to have had secret meetings with top Israeli officials.
If a challenger defeats May in the event of a leadership contest, he or she would take over as Conservative leader and as prime minister. A national poll is not necessary for that to happen.