@witherwings, you raise a very interesting point there. They noted a lack of 'seniority' as one of the reasons for backtracking on a verbal agreement that I could work part time.
Using my work as an example, that was actually age-based discrimination. I was an untitled solicitor who had been there for 8 years. No one in the firm had ever been promoted to senior associate when they were under 35. So what they were actually doing was restricting part time work to people over a certain age, which is illegal.