DVLA is ace!
I've been lucky not to have to call central government very often, but the one occasion I can remember it was the DVLA.
I'd sent my license back for a photo update only to find I had to travel to the US on business. I needed the license to hire a car.
I spoke to a nice chap at DVLA. Not a call centre because his Welsh accent was very obvious. Rather than mess me about he immediately passed me to his supervisor who was extremely helpful. She offered two or three options for me if they were not able to get the new license back on time, but she also promised to "look out for it and hurry it up". I must say I was a bit dubious - it seemed such a personal assurance to give.
Anyway, my new license arrived safe and sound two days later, and I had no problems hiring the car. Outstanding service - especially as the DVLA had a backlog of licenses to deal with because of the postal strike that was on then.
In total contrast was my attempt to ask Hertz (the rental company) if they would accept an official fax copy of my license from the DVLA (this was one of the options the nice lady there offered). Nobody there had a flipping clue! They were hopeless, and broadly speaking couldn't care less.
I'll still use Hertz in the US because they've got the best checkin facility at SFO, but I hope I never have a paperwork query with them!!!