All British Opens have been played on links style courses nearby to some big body of water beside course. Royal Dornoch, Royal County Down, Ballybunion are some notable courses that would seem to be excluded that fit qualification otherwise. Sunningdale being on outskirts of London is considered an inland course---not a links type course. Here is a list of rota courses that have hosted British Open and list that copy here has to be changed as a few years back Muirfield was taken out of rota for not having women members.
Current rota courses
St Andrews, Carnoustie, Muirfield, Turnberry, Royal Troon, Royal St George's (Sandwich), Royal Birkdale, Royal Lytham & St Annes, Royal Liverpool (Hoylake) and Royal Portrush
Former rota courses
Prestwick, Musselburgh, Royal Cinque Ports, and Prince's
By the way Sunningdale's Old Course was designed by twice winner of The Open Championship, Willie Park Junior and opened in 1901. The British Open was first held in 1860, so the length of the course being possibly 300 yards short according to Jimbo of providing a test for today's golfers is not at all a factor that should be taken under consideration now days as if tournament officials wanted to play this course as venue for British Open---they certainly had many years to choose a non-links type of course before now and 300 more yards would not be sufficient. Hole #1 is a 495 yard par 5, hole #3 is a 315 yard par 4, hole #9 is a 275 yard par 4, hole #11 is a 322 yard par 4, and hole #14 is a 499 yard par 5 making for 5 holes really playing extremely short lengths. Looking at history of course---Bobby Jones had great fondness for the Old Course. In 1926 during qualifying for The Open Championship (which he went onto win at Royal Lytham and St. Annes) Jones shot 66-68. Regarded for many years as the ‘perfect round’ the 66 consisted of 33 shots, 33 putts and no hole was played in more than four and on ten holes, the shot to the green was played with a two iron or wood. NOTE: THIS WAS IN 1926 AND COURSE IS LISTED AS ONLY AROUND 6600 YARDS by link currently shown here. https://www.provisualizer.com/courses/s ... course.php