For Meet & Greet parking at MAN & BHX, I have always used CPS (Chauffeured Parking Services). Website is
http://www.parkwithcps.com I have never had any problems with this company - they are always there to meet you at the stated time & are generally very flexible if you phone the given number to say you are running early / late for your departure meet. They have always insisted on walking round my car with me to agree on the condition of the car & mileage at handover (& make you sign to confirm this).
CPS also monitor your incoming flight - I once arrived on AA into MAN well over an hour early & phoned then from the baggage reclaim hall to advise of the early arrival. The response I got was "yes, we know the flight is in, the driver will be there in 5mins". Sure enough, we got outside (baggage trolleys laden with ski bags / equipment) and the car was there waiting in the arrivals pickup area, fully defrosted & warm (it was Feb).
Admittedly, I don't know where CPS actually park the car, but everything about them I have seen seems 100% professional.