When I've previously visited the National Archives there has been a rack in the locker room for storing suitcases of any size (they were chained to the rack). However, the evening before my friend and I were travelling to Kew, quite by chance she found some information on TNA's website which said that they no longer store cases over certain dimensions (see link)
http://www.nationalarchives.gov.uk/about/news/large-bags-and-luggage-not-permitted-inside-the-national-archives/I measured my case wrongly (forgot about the wheels, it was late at night!) and thought it was within the height restriction. My case is actually 50 cm high, we measured the locker on our first day and found that my case would should actually fit inside the locker. After some worrying on my part about being declined access, we arrived at TNA on the second day, on which we were leaving and found that my case was allowed in and did fit inside the locker My friend had bought a new case the morning before we left because of the published details so was not amused!
To give an idea of the size, my case which fit into the locker is standard airline cabin baggage maximum size. My friend asked whether TNA have any plans to change the existing lockers but was assured they do not as the locks have just been changed to keypads instead of keys. She filled in a feedback form on which she said that the website information was incorrect so perhaps they will correct it.
The change was apparently introduced in November 2017. New visitors might become aware of this as they will probably read the information about planning your visit, but those of us who have been before would be less likely to read it. I can imagine that people who have travelled a long way and have a large suitcase with them would be less than pleased to be told that they can't enter the building with their case! (Bag checks are made on entry).
The following link gives information about places that offer luggage storage:
http://www.nationalarchives.gov.uk/about/visit-us/researching-here/can-take-reading-rooms/The nearest is a convenience store next to Kew Bridge underground station, the next nearest are at Hammersmith.
I hope this information might save Rootschatters getting a nasty surprise when they arrive at TNA!
