Hi freddiestewart, welcome to the forum.
Your father would have been a member of the 1st Battalion then. Here's a bit of reading to get you started:
http://www.goldbeach.org.uk/english_...hampshires.htm
However, the best bet is to get a couple of books that detail their involvement and activities. The best two are:
http://www.amazon.co.uk/Gold-Beach-B...3517780&sr=1-3 http://www.amazon.co.uk/Royal-Hampsh...3517693&sr=8-1
I have the first one and will scan a few snippets for you tomorrow, and post them here.