Another thing is that older recovery vehicles, especially bus conversions, tended to use a tow bar. These days that's still legal but tends to be looked down on, so recoveries are usually suspended tow. Not surprising really, for bar towing you need someone in the bus cab to steer it and ideally operate the brakes. No engine means no power steering, and modern buses are almost undrivable without (the last Atlanteans, VRs and Fleetlines without power steering were bad enough, modern buses are heavier and the gearing on the steering is designed for power assistance). Not ideal either, the towing vehicle stops quick and unless the bus driver can get the handbrake on quick then it can be messy. Also it's no good if there are problems with the wheels or axles. Oviously though a proper suspended tow truck, whilst much better, is a hell of a lot more expensive than just chopping down an old bus.
Of cource TFL have their own fleet of tow trucks positioned all over London.
More to it than that, there's also the question of having a qualified HGV driver around (though I think I heard somewhere that a conventional tow could be done on a PSV licence).
Nowadays dragging stuff is rare because of the damage that can be done to transmissions if not done correctly.
Also, although I don't doubt TfL do have their own wreckers around the place, all the photos of failed buses I've seen have had a contractors truck doing the honous.