I can ony speak form my experience.
we lived in Kent, and started statementing with dd1 when she was 3ish - at MS pre-school.
a year later, with little progress overall, we had a proposed statement - up to 7 hours extra support.
It had taken so much chasing (blood out of stone stuff) that we knew it would be a massive fight ot get any more (dd1 was at preschool for 15 hours), and we had been turned down for the ASD unit - dd1's best chance for where we were at the time. the expectance was that she would go to the SLD school.
we moved.
it was the only choice for us and her.
so, moved ot Surrey, dd1 still in preschool (an ASD one htis time), but out of year - she should have been starting in reception.
Surrey re-started statementing, on the basis that 1) all the reports were out of date (thye were coming up to 18 months old, due ot Kent's procrastination); 2) dd1 was now in a specialist setting, so a reappraisal of her needs was due; 3) the old statemnt had been for pre-school, and we shoudl be looking at school placement/hours of support.
it took another 18 months of wrangling to finalise her statement.
genrally speaking, it will depend on what provision new LA has, and what space within that provision. also what you current statement says.
eg, if your statement is likely to say 12 hours support, and Hants statements routinely start at 15 hours, it is intheir interests to keep the old statment.
if, however your statemnt is likely to sya flltime 1:1 within a unit (extremely unlikely
) and Hants has no unit, so would have ot pay out of county costs plus transport to keep your ds at a place, when they have a provision within county that they think would suit, then they will reassess.
you could do worse than call them and ask, I suppose. but naturally take whatever they tell you with a large pinch of salt...