As a former Local Authority Licensing Legal Advisor, I can tell you that they could be acting lawfully or, more likely, unlawfully. A Council is entitled to charge to finance the cost of maintaining its licensing function. It cannot charge sums which are unnecessary for that purpose. Although it is correct that they can insist on a licensing regime for both Hackneys and Private Hire vehicles, as they are covered by different legislation, it is most unusual for a charge to be made and an extra licence to be required for PH if a HC drivers licence is already held. This is because the HC Drivers Licence is traditionally more difficult to get. (Knowledge tests etc). If you have satisfied their requirements as to suitability, health, topographical knowledge in respect of your HC, there is nothing else to pay for in respect of your PH except the extra paperwork which they are insisting on. Start by asking the Council officially how much they have raised from fees to finance the taxi licensing adminsitration function, split between separate sums for HC and PH. Then ask them how much each of these sectors costs to run. HC will invariably be more expensive to run as, for one thing, they have to paint up HC ranks which cannot be used by PH so PH should not be required to pay for them. There are two notable cases where Councils increased fees to raise money and the Courts have decided that they were wrong. In one case, they were told to pay the extra money back. I would be interested to know which Council it is and the outcome of your enquiries.
Incidentally, do you actually drive both types of vehicle or just HC?