It hesitates every single time you set off from a standstill, Citroen dealer couldn't be arsed to sort it properly so we've lived with it. "Sunshine" and higher temps arrive and the car switches on the a/c itself even though I've told it not to do that

Anyway, I left the a/c on thinking it'd give the system a nice workout and would you believe it - the hesitation went away, as in a completely normal drive and totally smooth

Predictably it's now hesitating a little with the a/c on but it's MUCH MUCH improved.
Scratching my head for ideas I can only loosely assume that when Citroen had the car in for "reprogramming" the gearbox then they did so with the a/c running? perhaps there's some compensation effect in the system for having a/c on or off? I don't know it's bizarre but kinda 'fixed' if you like.
We did 550 miles in it this weekend with 4 adults aboard and it didn't miss a beat, happily cruising at 70 plus 15 and civilised enough to be a comfy mile eater.