What's been said up to now has been about right.
A PSV can indeed ply for hire wherever it wants to (PCJA states that no vehicle can ply for hire unless it is displaying a PSV operators licence). The analogy would be back in the good old days when you went to the seaside there would be a line of coaches on the sea front offering tours to local places of interest. These service didn't have to be registered because they didn't run to a timetable or indeed every day. A similar situation exists at Dover Western docks where the cruise ships come in.
A pal of mine runs regsitered local bus service tours round dover from there; another pal runs a restricted licence PSV minibus from there, and the local cabbies were moaning about another minibus operator standing there plying for hire, going wherever you wanted. Questions were asked at the CPT and the answer is, it's legal.
What "could" make the Brum operation illegal is if the minibuses run a regular route, i.e. Bull Ring to a housing estate, stopping on the way to pick up or set down. That brings it into the registered bus service domain which as Grandad points out, is a kettle of worms.
There are 3 types of O licence for PSVs: "restricted" (orange disc)issued usually to taxi operators who can run up to 2 16 seaters and not require the financial standing of a full psv licence, and don't need a transport manager; "standard national" (blue disc) which needs financial standing, transport manager, and allows whatever operation you want in the UK; "international" (green disc) which allows the same as the standard national, but also to operate internationally. there's also community bus s19 and s22 permits used usually by charity groups and the like. these CANNOT be used for hire and reward and come under separate regulations.
What I'd suggest in the Brum case is to go bus spotting. see what O licence (if any) is displayed, note the operator's name and address which should be on the side of the vehicle, registration number and the like, and if it seems to be running regularly, reprt it to VOSA.
enquiries@vosa.gov.uk is the email address. They would be especially interested if as I suspect some of these minibuses don't display o licences. the other thing to look out for is whether or not tachos are being used, a neccesity for virtually ALL psv operations except certain registered local bus routes.
My company has O licences and a letter of authority from the Traffic Commissioner to run an under 9 seat vehicle on that O licence; it also has a couple of PH operator licences!
Edited to add that there's different types of sepaarate fares; graduated separate fares that you'd find on the local bus service, or one fare paid by each person such as that you'd find on a coach going from A to B. There's also private hire, where a single hirer could hire the vehicle from an operator and charge the people in that group the cost of the hire, Here, the person hiring the bus or bringing the group together must not be the owner or driver of the vehicle. The latter case would or should be the instance used in Brum.
There is also private hire where the vehicle is hired by an organisation such as a school where the passengers pay no fare.