there are massive interwoven society deep rooted problems. And studies show that women will prioritise work life balance (and that means less pay) whereas men will prioritise chasing the money
This. Unless the rate of pay is lower for jobs that have been objectively valued at the same level and/or women have been prevented from working in the higher paid jobs, as was the case in Birmingham city council (female cleaners vs male bin workers) or Asda (female shelf stackers vs male warehouse workers) then it's not necessarily Bristol city council paying women less due to their sex more a case of correlation not causation.
In my work department, however you measure it, women's salaries are higher than men's. Because our department head is a woman, most of the middle managers are women, as are the senior technical specialists and we have quite a few inexperienced technical, admin and facilities support staff who are men. So you could use this information to claim that we pay women more. But we don't - the jobs pay what they pay, according to a set pay scale that is almost never deviated from, just that we happen to have an atypical split between the sexes.
The problem is society and if you want to use it as an illustration of women being disadvantaged, the problem is that women disproportionately take on more domestic work, so have to factor this in when deciding what type of paid work they are able to commit to.