I do hope Churchill doesn't sack the responsible person, as I have suspicion it might be... *dun,dun,duhhhhh* - You! Partially at least.
I gather you are playing as you go in short-ish bursts, there are references to attacks stoppping after reloading, etc. Now as I understand it the HOI3 AI, particularly the Theatre assignment part, doesn't do well under those circumstances. Everytime you load up a game (or TAG across without pausing) it re-runs the 'What forces does that theatre need' routine and tries to ship forces out, subject to various priorities like protecting the capital, etc. If you are always re-starting, this is always getting re-run and the process reset, this is particularly bad if the force moves are by sea as naval forces are more prone to getting re-routed by the AI and/or just sent home instead of continuing their journey.
Of course this being Paradox you must be careful not to play for too long, or the Theatre AI can get stuck in a different bug and not reinforce anything, you can see this if after a restart it suddenly surges forces to an empty front. A quit and re-load every 6 months of game time was reportedly the 'best' balance, but it depends on what sort of AI you want to face.
Finally it is also possible that none of the above matters in this case. It is alleged (but impossible to prove) that the Theatre routine is incapable of differentiating between HQs and proper units, so the British AI may see those many HQs as effective combat units and not be trying to reinforce. This is plausible as people are fairly sure the HOI3 AI cannot tell the difference between other unit types, hence why you see Armoured divisions attacking mountains, mountain divisions dumped on tropical islands, Marines not leading amphibious assaults but being in the 2nd wave, etc. But surely Paradox couldn't be that inept... Surely?