Sophie
, that's harsh and uncalled for. Even at that age there are some kids who are so far beyond (or different to) the development of "normal" that they need appropriate help for their development, just as much as the kids who need help to achieve "average". All kids deserve to be able to access an education suitable for their level of ability, and that includes ALL abilities, even the very able.
OP, why can't the assessment be done through the nhs? When my DS1 was assessed (twice, once at 3 1/2, again at 5 1/2), it was organised with our consent, through the preschool and through the primary school and we didn't pay anything (Scotland, so maybe different).
The Ed Psych came into the school and carried out (long!) assessments there, and afterwards recommended extension work and other adjustments (which the school refused to do btw, and eventually we changed school to get him what he needed, but that's another story!).
I think that if pre school is activity pushing you to assess before school starts, the HT suspects that your DC isn't just bright, but is exceptionally bright (because G&T is only the top 10% as I understand it? We don't have G&T in Scotland).
Maybe you need to discuss it some more with the HT and clarify why they think it needs to be done now, and why privately.