Following Michael Fallon's resignation as defence secretary, May yesterday outlined new procedures for dealing with allegations, as further claims swirled around Westminster.
Her governing Conservatives will adopt a new complaints procedure with a hotline for reporting potential breaches, and officials want the measures replicated in other parties.
May's announcement follows the flood of sexual assault and harassment claims against Hollywood movie mogul Harvey Weinstein. Those revelations prompted allegations of inappropriate behaviour in Westminster -- with several allegations of misuse of power surfacing.
May is due to meet leaders of other parties on Monday to thrash out a cross-party approach, saying it was not right that "vulnerable or concerned people" could be left to "navigate different grievance procedures."
"There needs to be a common, transparent, independent grievance procedure for all those working in parliament who wish to raise concerns which provides clarity and certainty about how their concerns will be dealt with," May said.
The new Conservative code applies to the party's elected representatives, from MPs to local councillors and city mayors, and party officers at all levels.
Fallon quit as defence secretary on Wednesday, saying his behaviour had fallen short of the standards required. He admitted touching radio presenter Julia Hartley- Brewer's knee 15 years ago -- an incident she said was nothing other than "mildly amusing".
According to The Sun newspaper yesterday, Fallon's resignation was actually prompted by complaints against him by Cabinet colleague Andrea Leadsom.
But a source close to Fallon told the tabloid he categorically denies telling her at some point between 2010 and 2012 that he knew where she could put her cold hands to warm them up.
May's Downing Street office then issued a statement saying Leadsom "did not, and has not, asked the prime minister to consider the position of Sir Michael Fallon when he was defence secretary".
May replaced Fallon on Thursday with another loyalist, chief whip Gavin Williamson, who had been in charge of enforcing party discipline.