It would make more sense to plaster the George Cross all over trains that operate wholly within England, and the union Jack on cross-border services. But the DfT would never go for that, as the UK Government has a complete inability to say England when an organisation only (or 90%) serves England.
The only time you'll see the UK Government owning the English flag is if England are in a football tournament. The rest of the time, anything that is 90% or 100% English, is "British" in the mind of Westminster politics.
Hence why we now have GBR and the Union Jack plastered all over trains managed by the DfT in London.
Gareth Dennis has just done a very good Railnatter on what the organisation and liveries of GBR should actually be, including a distinctly branded Intercity sector of GBR.