I can show how I get HQ photos from the site...here is how...
1.for example..On this page with Queen Mary photo http://www.royalcollection.org.uk/collection/2000432 point yous mouse arrow on either left or right side with the baby blue color (which is frame of the page)...you will get a drop down menu.
2. From the drop down menu Select SAVE PAGE AS and click on it.
3. another window will pop up titled SAVE AS, which is the location that your link will be saved as...(normally all the photos go directly to the main PICTURES file which is on every computer.)
4. on that same pop up window on the bottom you will see two slots (boxes with the drop down arrow on the right) FILE NAME (which will have the original name of the file...you don't have to change) SAVE AS TYPE
5. In the SAVE AS TYPE you need to click on the drop down arrow on the same line...you will see selection on how you want to save...on the drop down list choose WEB PAGE HTML ONLY and then click SAVE.
6. If you are using Internet Explorer you need to go to your PICTURES file and open the saved link, which will give you HQ photo... IF you are using FIREFOX you will have a pop up window after clicking SAVE< which is the DOWNLOADS window...its like a short cut to get to anything you download on your PC...all you have to do is double click on the file in the download box and HTML page will open which will look just the same as the page on the actual website.
7. click on the photo twice and Voila..you'll get your HQ photo just like the one on the bottom...don't forget to save it to your computer