Please do credit the Royal Collection if you post their pictures. I don't think they would be happy about the spreading their images without crediting them.
Here's what the Royal Collection website says:
The website and its contents are owned and operated by the Royal Collection, part of the Royal Household. All elements of the website and all rights therein, including but not limited to the content and general design, are protected by copyright. Some content displayed may also be subject to third-party rights.
Published by Royal Collection Trust / © HM Queen Elizabeth II 2012
By accessing this website and downloading or otherwise viewing any images or other content from this website, you will be deemed to have agreed to the following:
Any commercial use of the images on this website is subject to written permission from the Royal Collection and the applicable Licence Terms and Conditions displayed on this site. In particular, but without limitation, no images may be reproduced, communicated to the public, distributed, re-used or extracted from this website for commercial use (including without limitation any storage, reproduction, linking or indexing for the purposes of any search engines) without the prior written consent of the Royal Collection. Third-party permission (for example from the artist or their estate, or from the holders of any trademark, personality or image rights or similar) may also be required, and the Royal Collection makes no warranties or representations in this regard nor does it purport to grant any such rights. Please contact the Picture Library for further information, picturelibrary@royalcollection.org.uk.
To the fullest extent permitted by English law, and unless otherwise expressly agreed by the Royal Collection in writing, the Royal Collection shall have no liability in connection with any use made of this website or any images or other content contained within it.
I don't think they want them spread at all since they've attempted to disable some downloading ability. It would probably be best to just post links to the relevant photos. That should avoid the problem, allow the photos to be shared (as they are wonderful) and, in the future, if the photos become disabled it would prevent the endless red x boxes we have on just about every post.