I had the same problem getting details about my Father's LAA Regiment war diaries. If you telephone the National Archives as I ended up doing, they gave me the details of the relevant diaries reference numbers without any problem.
There is also some basic info on a site I found and if you click on
RA 1939-45 20 A/Tk Rgt it will take you directly to the section about 20th Anti Tank Regiment R.A.
Good luck.