I think Head of Training is an officially recognised position with defined role along with Accountable Manager, etc. by the UK CAA and EASA.
I don't think the CAA have ever given an official recognition to the title 'Chief Flying Instructor'. Of course, in the FAA system CFI stands for 'Certified Flight Instructor' so there's confusion, straight away.
I've known people call themselves Chief Flying Instructor in a small group of five pilots owning a C172, without having any further qualification above PPL.
I sign myself Head of Training when corresponding officially but I also answer to Chief Flying Instructor if circumstances just make it easier. If someone persists with the title officially, I'll revert to HoT and explain why.
TOO
TOO