The following site gives a great deal of information about the RA and how individual regiments were allocated. Extract below re 20ATR
British Artillery in World War 2 20 ATk Regt Reg
Fm 20 Fd Bde 1938 France 1939-40 - 3 Inf Div
UK 1940-4 - 3 Inf Div
DDay 1944 - 3 Inf Div
NW Europe 1944-5 - 3 Inf Div
The Regiment's War Diary will be in the National Archive at Kew. Knowing the Division will help to scale down the search. Good Luck
Jim