The next morning I get a call from a rather rude operator - just minutes before they were scheduled to pick me up - telling me that I haven't paid the full amount for the ride. I told them that I booked using their website and paid online with PayPal. He replied that he doesn't know why the website didn't show the correct amount but if I don't pay an additional £30 to the driver they won't give me a ride. I agreed because I just wanted to get to the airport asap and not deal with finding another company.
The lesson I learned here was: I don't trust minicab companies to be able to deal with the tech behind something like Uber. Of course, this was just one bad experience with a single company but it did leave a bad taste in my mouth.