We got a taxi the last time booked in advance, got met as we left arrivals by the driver, and for 2 of us only cost £5 more than it would have on the magic shuttle.
PS. our flight was in after the last shuttle which is why I looked into taxis in the first place. Won't be getting magic shuttle again, taxi was much more convenient, quicker and more comfortable, and for a family of 4 would be significantly cheaper.