Even if the OP had checked before he started, as you suggest, he would have found the following information for Sharpness Dock on the CRT website.
"We recommend you purchase licences on line, and in advance of your journey, to save time, however visiting craft may also pay by cash or cheque on arrival at the port."
https://canalrivertrust.org.uk/about-us/our-regions/south-wales-and-severn-waterways/sharpness-port
I have every sympathy with the OP. The Bristol Channel is a dangerous place; it's not somewhere where you want to be suddenly forced into making an unplanned passage due to being denied entry into a port.
CRT need to address this problem before there is an accident.