The cost of UM travel is actually a lot less than it was a few years ago!
Before we intoduced the UM fee, the UM had to have a "Full Adult Economy Fare" ticket (either a full "S" or "Y" fare basis for long haul, or a Full Club Europe (C class) for European short haul or an "M" fare basis for Domestic.
(That would have equated to a return fare of at least £750 for most long-hauls, £450 for most short hauls and about £100 for a UK Domestic service.)
The reason for introducing the UM fee was because several private schools were buying discounted tickets and sending the children to the airport by taxi as "unnotified UM's", where they were handed over to the airline as a fait accompli. When children are excitedly handed over expecting to go home to mummy and daddy for their holidays, it would be very nasty of the airline to send them back to school with the taxi driver!
BA decided to revamp the Skyflyers Solo service, developing tighter controls and charging a fixed fee. However, given the litigation that resulted from our policy of not seating single males next to an UM, the high cost of providing escorted hotel accommodation when children get stuck somewhere en-route, the heavy cabin baggage that parents expect BA staff to lift because they "don't want little Johnny to wait for a bag in the baggage hall" and the plethora of other hassles and costs that BA endures, I am very, very surprised that we still carry UM's at all.
As far as I am aware, no other airline carries UM's with the same responsibility as BA. (Most airlines have stopped the service altogether, and the few that still do have hefty fees and disclaimers written into their conditions.)