Being charged waiting time in Black Cab whilst I am still trying to get in?

Ask away Helina :-) 

Hi @Helina and welcome to the community. May you ask a question? You may ask as many questions as you like  Looking forward to hearing more about you.
Best wishes,
Richard

Hello again, @Helina. Very good to hear from you.
Okay, this is not in any way my specialism, but I have no doubt there will be plenty of others in the community who have had a similar experience and will get back to you.
An online search produced this:
https://www.gov.uk/transport-disabled/taxis-and-minicabs
Essentially this tells you who to complain to and, presumably, you would be able to get legitimate advice about correct fares from them too. I also found a couple of blogs within Scope, a starting point for you might be to type the phrase Black Cabs in the Search box at the top of the page and see where it leads you.
A I said before, I am sure others will get back to you but if the information I've given you leaves you still stuck or you don't get the answer you need, just drop me a line here and I will try to look into it further.
Please don't think twice
warmest best wishes, always,
Richard