Kindle, the Royal Hospital is immediately by Chelsea Bridge!!! If you are coming from Vauxhall direction, then as you go past the lights at Chelsea Bridge, then the grounds are on your right! About 500 yards down on the right hand side are the gates you want … in a cut out hence the ‘Bull Ring’ name 
You can’t miss the Hospital once you get to Chelsea Bridge. It is immense. I would love to go there just to chat to all the Old Boys in there!!