Welcome to the forum, mattwardle.
As it so happens, I am Saudi, born there, and have lived there almost 1/2 of my life.
Saudi Arabia is a very unique culture, as you will find out for yourself. There are too many "apparent" contradictions and you have to be
ultra conservative.
Photos in public are, generally, frowned upon .. especially if you're male shooting in public where people frequent. However, you can do it, but you have to understand the customs of the people.
Saudis individuals give very high regards to their privacy and family's privacy. So, if you're going out to shoot in public, just be careful not to get any of the females in the pictures. As a matter of fact, try hard to avoid carrying your SLR in places where women would want to be walking about (you will find lots of places where women don't go, and where women do like to hang-out).
Religious police are the Vice-Police too, and they have a lot of say and authority. You never want to get on the wrong side of these individuals. If you see them coming, don't run away, don't turn away either .. that will make them suspicious of you (most of them are very weary of Westerners as it is, and you don't want to aggravate that any further). Just be calm, and see if they want to speak to you.
If they do, respond politely and in most likelihood you'll be off your way sooner than you realize. They can be friendly. If they want to confiscate something off of you, be calm about it and make sure that they know you're from UK (Saudi Government has a very high regards to individuals from US, UK, and a few other Western countries ... we try very hard not to upset people from these nations .. something for another thread, though). If they persist, tell them that you will gladly show them what's on the memory card, with you present, and that you will be happy to delete anything they find offensive (keep in mind, what you find offensive will always differ
big time with what they find offensive). But, be agreeable .. please.
Regular police are, too, very weary .. but not of Westerners .. of anything out of the norm. You will see, once you are there, that people with cameras in public is not a common sight. Even though everyone will be carrying a mobile phone with a built-in camera, no one would dare use it in public (keep in mind that the authority did have mobile phones with built-in cameras banned, at the early stage of this technology, but only conceded when they realised that all phones would have this). SLR in public is not common at all.
I used to go out very early in the mornings to do my shootings, and found that the normal police were just always curious and then they leave me alone. There are wonderful things to shoot, very different from here.
As a matter of fact, I only had one incident with the police and photography, and that was up in a city called Taif. It's a mountenous city, and I was shooting off a cliff down a valley. Apparently, someone living down the valley saw me and notified the police, who came demanding that I pull out the roll and hand it to them (this was in 1985). I refused, and it got really nasty. In the end I was allowed to go only because they "sympathized" with my lack of culture knowledge even though I am a Saudi (it was a very close call that could have landed me in jail).