I've just bought some white Thassos pebbles for the flower bed. Do I need to use a natural stone sealant to protect then and maintain the look, or is this just for natural stone slabs?

Hi & welcome! Is it your intent to use the rocks as mulch?

If you are planning on using it in garden beds then it will rapidly change color. It will be nearly impossible to keep them white.
Once they are in contact with the ground they will be easily stained by both soil or dirt and by alagae.
If you clean them every spring they might look good for a year. But it will need to be done most likely on a yearly basis.
It might be a good idea to research how to clean them before putting them down but my guess is that they are already in place. The problem lies in the fact that removing them to clean them would be quite a chore. You could spray them possibly with something like Physan but you have to determine if that will cause harm to the existing plants.

Thank you both for your responses. They are on top of weed control fabric, on a bed with some buxus balls. It rains a lot here too, so not sure if that makes a difference (for better or worse!).

Happy to suggest. In the opening, you referred to this area as a flower bed but it is going to be difficult for flowers to grow with the weed fabric in place.

Sorry I'm still getting used to all this gardening stuff as I've never done it before. It used to be a flower bed, which the previous owners didn't maintain. So we've dug it out and put down weed control fabric and planted buxus. We don't intend to add anything else to this area.

That makes more sense. I wish you the best! : + )

Some of the commercial landscapes here use stone and shrubs, it is a very clean look. I would try to keep it blown clear of any leaves or other debris that will hasten any stains on it.