There seems to be a window between arriving and being properly in the public system, and I keep reading it's where people get caught uninsured. How did you bridge it?
Private cover for the arrival gap, then transition once you're in the public system. The in-between is exactly the risky window, so don't leave it uncovered to save a month's premium.
As retirees our route into cover was different again — it really does depend on your status and nationality, so don't assume your friend's path is yours.
Whatever you do, don't cancel your old cover until the new one is active and confirmed in writing. The overlap costs a little; the gap can cost a lot.
Freelancer here — I kept private cover longer than planned because the paperwork to get into the public system lagged. Budget for that overrun, it's common.
"Private for the gap, don't cancel the old until the new is confirmed." That's the reassurance I needed — thank you.