Presumably you think that all membership clubs should be banned as by definition they exclude many people who apply? What about boys or girls only schools - that's discrimination isn't it? How about nightclubs that bar people from entering becuase they're not wearing the right clothes? I could go on.
You are in the UK. Membership clubs here are already subject to laws that prohibit discrimination based on protected characteristics—those characteristics that make a person who they are and they cannot change. There is no reason to ban those places if they discriminate based on a selection process that takes into account other irrelevant characteristics.
I think that single sex schools are discrimination. From the studies I've read, there are no significant benefits by separating boys and girls and so I believe there should not be an exemption for them.
Clothing is not a protected characteristic. It doesn't define who you are. If you're wearing the wrong trousers then go home and change. If you're black, disabled, a woman, or are gay then it isn't possible to do the same.
The fact you can't seem to see the difference between discrimination based on factors that make a person who they are and those that are petty, such as their clothes, suggests you don't know what you're talking about.
Do you believe a black man should be denied equal service compared to a white man
because of the colour of his skin?
Do you believe a woman should be denied equal service compared to a man
because she is a woman?
Do you believe a disabled person should be denied equal service compared to others
because that person is disabled?
Then why do you believe a gay person should be denied equal service compared to that of a straight person
because they are gay?