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"Your point might be more relevant if these statistics weren't comparing like for like. No one who works at CMS or Shoosmiths studied 'feminist dance therapy' or 'electrical engineering'. They all studied law."

This data doesn't show like-for-like. It shows average pay per contracted hour of employment. This has two big problems:-

1. Women are more likely to occupy more junior roles in a law firm, because (i) secretaries are more likely to be women, (ii) more women are now qualifying as solicitors than men (so the proportion of NQ women is bigger), and (iii) men are less likely to take a permanent career break (so are more likely to still be there are 10PQE+) [query why that is, but that's not the point of these statistics]

2. Full-time employees are more likely to do more unpaid overtime. That is probably factored into their salaries but is disregarded in these statistics.

You therefore end up comparing a 40-hour-a-week secretary on just-above-minimum wage, with a 10PQE senior associate who does regular all-nighters (and is paid with that in mind) but also shows up as doing a 40-hour-week in the statistics.

I don't doubt that there are problems for female representation at senior levels of this profession. But I do doubt whether these statistics tell us anything meaningful from which we can learn.