Not sure where in Essex you are, however your experiences sound all too familiar with my own - as someone who volunteers for an Essex based charity and was approached to assist setting a mans shed up. Initially I offered to use my own workshop on a limited invite basis, however they -the Mens Shed association have strict rules on this and they preclude any 'shop on private land. The charity appear to have access to a lot of donated kit but because of bureaucracy and the charities entrenched 'decision by committee' approach - where most committee members are quite frankly clueless, they have made little progress in the ~3 years that this subject was floated.
Hats off to those who do have access to one that is well run/organised and provides the social, learning and practical skills that folks want, I personally have given up trying with the lot I'm affiliated to, and gender discrimination doesn't even enter into the equation although I guess I am unsurprised at your unfortunate experiences...