I posted this in response to a question on another thread, but I think it's appropriate to post it again here as an info item.
Arab News, Feb 12, 2013
The British Embassy announced yesterday changes in the passport service for British nationals living in Saudi Arabia and elsewhere outside the United Kingdom.
“British nationals in Saudi Arabia will be now required to submit their passport applications to the Ideny and Passport Service in the UK and this will be effective from Feb. 11,” said a spokeswoman of the British Embassy.
She said that the application process had been centralized for the British expatriates. The change follows reviews by the UK’s National Audit Office and is designed to achieve economies of scale, greater security and consistency in decision making, she said.
Another question on this, although a bit more general, if you renew your passport out of the country (i.e., say when in UK) is there an issue entering SA if you have a new passport and your visa in the old passport?
That's true, my wife renewed her passport when she was out of the kingdom one time. On re-entering (carrying both passports) it was a simple matter of an extra 10 mins or so for immigration formalities - we had to go to the supervisor's office and it took a (surprisingly) short amount of time to transfer the residence visa info from the old to the new passport.