This link takes you to the Liverpool Records Office archive of items relating to 106th RHA. http://archive.liverpool.gov.uk/dserve.exe
There are also 2 books by Douglas Arthur:
Desert Watch tells his story of the outbreak of war, call-up, training and his battery's time in the desert up to the battle of Beda Fom.
Forty Men, Eight Horses picks up the story in Greece, covers the massive losses when the Slamat was sunk, moves on to the Battle of Crete, capture by the Germans and then time as a PoW
I gather the link isn't working properly - try using this linkhttp://www.liverpool.gov.uk/libraries-and-archives/archives-local-and-family-history/
click on Liverpool archive catalogue and type 356 RHA in the search box