You probably need to check the REME Workshop war diaries at TNA (or ask some kind soul to do so on your behalf) but as far as I am aware 109 HAA Regiment (and its attached REME) were part of 107 Anti Aircraft Brigade which was under command of 2nd 1 Canadian Corps from December 1944 through to VE day. I think the Anti Aircraft Brigade would have been under direct command of the Divisional or Corps Headquarters. This forum article indicates that 109 HAA Regiment were part of the 2nd Canadian Corps in April 1944, but doesn't mention the name of the intervening brigade they were part of at that time:
https://forum.axishistory.com/viewtopic.php?f=114&t=233555&p=2122793#p2122793 As your original question was about the unit in June 1945, that is to say, after VE day, I would be fairly surprised if the unit (109 HAA Regiment) hadn't reverted to their national chain of command by then, so the Canadian Corps may well have dropped out of the picture.
The definitive history of the Anti Aircraft Regiments in WW2 is:
Brig N.W. Routledge,
History of the Royal Regiment of Artillery: Anti-Aircraft Artillery 1914–55, London: Royal Artillery Institution/Brassey's, 1994, ISBN 1-85753-099-3.
Sadly I don't have a copy but you might be able to get it on an inter-library loan. Alternatively the RA Museum at Larkhill may be able to provide more details.