Don't ask don't get !
Listen if a GP doesn't want the hassle and wants to pass the buck to a clinic they will, and its good practice, but waiting lists are looong. However, if they want to help you, my experience shows they have the wiggle room and remit to do that.
Never had levels done, told they are just a snapshot in time(in that moment)and told they are not worth doing.
I go by my symptoms, the main ones being insomnia, hot flushes, migraines, and extreme dry mouth.
If I control those everything else is covered too.
TD