I take it you mean World War 2.
World War one information is now fully obtainable and can be found on most family tree research sites.
World War two personal records are still restricted and wont be released until sufficient time has expired normally 100 years.
I think I am correct in saying that the only place that you will find any personal records of him is through the Army Records Office via gov.uk/get-copy-military-service-records
You need to be able to prove that you are related and obtain a Death Certificate to prove he is not still alive or he has to apply for them in person. It costs about £10 the record application is about £30.
I did this a few years ago for my uncles one of whom served in the Royal Signals in North Africa and Italy. For this you will get the records of his movements for administrative purposes, lists of transfers to other places i.e. hospital (a common one when taken ill) or embarkations to various countries, not lists of battles or where he actually was. They enclose sheets of explanations of Army jargon and abbreviations. These can be quite daunting. There is a long waiting list for replies at the moment.
You could also research his regimental history on line using a search engine. None of the sites charging you for this can do any more than the free ones. You might get in touch with the Regiment he was in through a Regimental Museum if you are lucky (again use a search engine to find them).
This site may also be helpful as members were there but bear in mind that they are of the age of your great grandfather if they were. Their relatives might reply with useful information they have collected.
There is also the National Archives website where you might find the Regimental War Diaries and lists of those who earned medals in combat, they charge for some of these records that are off line. The Imperial War Museum may hold photo’s of the Regiment in Action and allow certain photo’s free download for non commercial purposes. Search IWM website British Army Italy or Tunisia or North Africa.

Hope this helps and good luck.

Chris