There is no producer of starter sets in 3 rail O British outline.
The easy answer is Hornby OO (4mm to the foot) gauge which is what most British kids start with.
I had Hornby OO as a kid but I don't think it is the best for children.
To put together a 3 rail O gauge set from British equipment will set you back a few quid. ACE trains, Bassett Lowke etc. Cheepest loco £300 aprox. Plus the track a few
wagons (freight cars) and a transformer (Ace, Bassett tend to be 12V DC)
That is a very expensive train set.
It would be best to send over a US set. How about the Lionel Hogwarts set as it is British outline.
A few words of caution.
If you choose a Lionel set make sure the CW-80 transformer is the latest version with the "QC50-OK" sticker showing that it will work on the 50Hz power here in the UK. You will need a 230V to 110V step-down transformer to run the CW-80 from the UK mains.
DO NOT choose a set with Lionel TrainSounds as this system malfuntions on 50Hz.
RailSounds is fine (Not sure about the new Railsounds RTR, will need to check with Mike or jon at Lionel)
MTH gear is fine a Z1000 for example can have the US power brick replaced with
a 230V to 18V Brick. This is what Dave does Down Under. I would think it would also work with the US brick with a stepdown transformer as I have seen MTH's Z4000 run
this way here in the UK with no problem.
Hope this helps
Regards
Nick