CSP is an independent trade union in its own right, as are Unison, the Society of Radiographers, Unite, GMB, RCN, etc, etc.
www.gov.uk/government/publications/public-list-of-active-trade-unions-official-list-and-schedule/trade-unions-the-current-list-and-schedule
Most unions are affiliated to the TUC:
www.tuc.org.uk/how-tuc-works-unions
Most (all?) UK Trade Unions seem to be captured at policy level and "political activists" within unions virtue-signal like fury, as the Unison vote demonstrates:
www.mumsnet.com/talk/womens_rights/4570043-unison-passes-policy-trans-equality-louder-and-prouder
However . . . this does not necessarily play out in the workplace, where Reps/Shop Stewards are not always "political" activists but are more interested in collective bargaining and representation of individual members.
I am in Unite - which appears on the surface to be at least as badly "captured" as any other union.
Despite this, the feedback we are getting in the Unite GC Women's Group (part of the Women's Trade Union Federation) is that women are getting good, effective representation by Unite Shop Stewards when there are issues to do with "women's rights vs trans rights".
(WTUF: twitter.com/WomensTUF)
Similarly, I know of Unison Workplace Reps who are GC women and are challenging employers on anti-women policies and practices.
Unions seem to be doing everything in their power to lose the confidence of women but find out what is happening at local level before you give up hope.
Membership involvement in trade union democracy has been pitiful for decades, which allows take-over by narrow interest groups.
That also means that it is relatively easy to wrest back control if members get organised and vote in the representatives that they want.
That is what we need to do because nobody is going to do it for us.