2.5 weeks for the SO to get her UK passport renewed, including time taken for previous passport and supporting docs (ZA marriage certificate since she's finally putting it in her married name) to be couriered from NZ to the UK and for the new passport to be sent over. Actual processing time in the UK was 4 working days; much of it was courier time (and the fact that, if counting intermediate stops, the couriers used the world's longest flight).
The timeframe mentioned above to renew a NZ passport is about correct if renewing via the standard service (up to 10 working days). There's also an urgent service (up to 3 working days) and a same-day emergency call-out service, for which costs are obviously significantly higher: $191 for standard service, $382 for urgent service, $775 for same day call-out.
Meanwhile, the South African High Commission in Wellington is quoting a minimum of 6 months for a passport renewal.