Prospect is one of the largest trade unions representing staff in parliament.
The new report backed calls from the unions to introduce a process that is independent of MPs and for historic cases to be able to be considered.
Prospect deputy general secretary Garry Graham said:
“This is a really strong report that should be the final nail in the coffin of the outdated culture in parliament that has allowed bullying and harassment of staff to go unchecked and unpunished.
“Dame Cox is right to back calls from the unions for a fully independent process that is able to consider historic claims against MPs.
“Parliament is fundamentally a place of work, it is time for those with responsibility to reflect on this report and put in place a new policy and culture in keeping with modern workplaces that puts the safety and wellbeing of staff first.”