Apoca have had phone pay facilty for ages and they charge (or used to, not looked lately) 20 p for the "convenience" of using the the facility.
That is quite an interesting point, that will lead me to deviate from the thread's topic slightly. The car park at Hayes & Harlington is ^2.80 or ^1.90 (depending on time) if you feed the parking meter (which was broken last time I was there), the same price (with no fee) for paying by phone to Apcoa Connect BUT ^2 all day if you buy at the ticket office (and they accept credit/debit cards). The only issue is that the ticket office is a real trek from the car park. Confused the hell out of me. In other Apcoa Connect "implementations", such as First Capital Connect, they do charge a transaction fee.
Back to the original topic. At London Midland stations, Meteor parking have had online parking purchasing available for some time. They specifically state "Please note: Purchasing any tickets/permits in advance does not guarantee you a parking space". Their parking meters take credit/debit cards anyway, so it wasn't of much interest to me when I used Bletchley. I'm guessing it could be useful for adding extra time to your vehicle if your trip keeps you away for longer than planned.