Some payphones I think. Usaually non-BT public call offices, those in some London Transport (LRT or whatever today's name is) stations, some railway stations and so on.
But many 0800 may simply be barred, ratrher than chargeable. Although Childline's is required to be available.

8) 8) 8)

All calls to 0800,0808,0500 numbers are free.Except where they are barred as explained above,or or where they are barred by the carrier because they are a calling card service!!! They are normally chargeable when you phone them from a mobile.(Unless you have an Orange Contract Phone,and they can charge you if you are calling a cheap call service.)