Council License Fees even on private land?

by Aadam
(Birmingham)

Hi,
I am in the process of trying to set up a food trailer in Birmingham. Currently the council have no licenses for the town center and charge approx 250 per month around the city (if pitch is approved).
I have approached a local supermarket with really good footfall to make attempts to use their carpark. I appreciate there might have to be an application to change the license on the land use.
My issue is; i spoke with the local council and they said i would still need to pay the monthly street traders fee even if it is on private land. They claimed as customers will be coming from the highway the street traders fee would still apply.
Is this accurate or am i being misinformed?