Sounds like they could save money by sending some nhs patients to your private GP...
They need to get the infrastructure in place and thought through more though - I've missed appointments in the past because the first I knew of the appointment was when the 'You missed the appointment' letter came through. It had been sent first class - the letter about the appointment was sent second class and they'd taken a week to get it into the postbox.
In one instance it was for an appointment that was needed as a result of a complication after ds2 was born and there was probably a 2-3 week turnaround from when they said that I would need the appointment to when I would have had it (and then a week beyond that for the letter to turn up!) so if they had sent the letter reasonably quickly after sorting out the appointment for me I would have had it in time before the appointment. However it seems their system at the time was to book the appointment for you, then the letter got put into an admin person's in tray to write and sort out... Bonkers.
But if there were even 10 of those sorts of appointments made a week, where the letter didn't get sent out before the appointment happened, and that's just in one department, you can see how quickly appointments get wasted unnecessarily 

I've also had an appointment that I almost missed out on - I was sitting there waiting to be called, checked with reception a couple of times as it had long gone past the time I was due in but didn't want to hassle them too much as I know that there are times when appointments need to overrun. Eventually the doctors came out, I stood up to go in expecting to be called - only to be told they were leaving as I had missed my slot. When asking why, as I had been sitting there since before my time to be seen, turns out that they hadn't come to check in the waiting room if anyone was there because they could hear that there was nobody there - there was no talking or noise. I had been alone (apparently people usually bring somebody with them so there's chatting!) and reading a book (so not on the phone talking or playing beeping games) and they hadn't checked on the system either. They also told me they wouldn't offer me another appointment as I'd missed two appointments (see above!) so I dragged them down to the receptionist's desk to get them to confirm that I had been there on time and so I hadn't missed this appointment, plus I'd got the other letter with me, that was dated after the date of the appointment, to prove why I'd missed that. So they grudgingly said they would do the appointment there and then (and cut into their lunch time!) but in hindsight I wish they would have let me make a new appointment as it was a very quick and perfunctory appointment that was very unsatisfying and left lots of questions unanswered.
I've also had GP appointments that I've been at but had booked the last one of the day, only for the GP to have not got any appointments preceding it, so not scrolled down to see the end of the day and then gone home thinking that they had finished...
So while patients can miss appointments, there are times when this is the fault of the system which they need to fix themselves.
I also think that maybe if some appointments could build in a little flexibility into the system so for example, if somebody turns up early and somebody turns up late, the system could automatically switch their appointments over to reduce wasted time.