A few companies still have their own recovery vehicles, but not many now. Often they were converted from buses, cut down double deckers being most common. The problem is the cost of keeping them, tax, MOT maintenance, and also the training costs (no use if you don't have at least one member of staff who can drive it).
One thing these days is that buses, like trains, tend to be more reliable, but when they do break down there is often much less that can be done. Many problems also require a lot of skill, knowledge and equipment to deal with. Also in both industries, things to get you home, and expecially to get the passengers where they need to be, tend to be very much frowned upon. To be honest though in both cases it's often warrented, given the different environment today, including higher speeds and more traffic.
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.
