Hi Pete,
I don't have a current sub for Ancestry, but checking the National Archives shows that the war diaries for 53 Heavy Regt RA have not yet been digitised.
If you would like to search TNA holdings, be sparing in what you type into the Discovery search, as too much detail may mean than that some of the diaries don't show up in the results. Since you are interested in the period from June 1944 to VE day (and maybe a little after that) then the diaries you want are in WO 171. That should be your first filter term. Then in the main search bar just type '53 Heavy'. That will bring up all the relevant diaries, namely;
WO 171/1037 to 1041 for 1944
WO 171/4878 to 4880 for 1945
and in case you need it, WO 171/9091 for 1 Jan to 31 Mar 1946
Obviously if you aren't able to get to TNA that information is of limited use. Since the war diary files are big, I don't think asking TNA to make copies for you is a viable option as it would be expensive. Almost certainly some military historian will have previously made copies or extracts and so a detailed Google search might just turn up something. Alternatively, go on one of the many forums which deal with either WW2 in general or specifically Royal Artillery matters. I can highly recommend the RA section of
WW2Talk forum. Also, take a look at the
Royal Artillery in World War 2 website.
When searching generally be aware that 53 appears in the name of several RA units including a Field Regt, an Anti-Tank Regt, three Anti-Aircraft Regts (light, Heavy and Driver Training), and a searchlight Regt, and the word Heavy appears in the titles of a lot of Regiments (eg Heavy Anti-Aircraft, and Super Heavy).