Hi Antony,
Have you found your grandad in the 1939 Register? That should tell you what his occupation was. From that you may be able to work out if he was in a
reserved occupation and therefore unlikely to have been called up to serve in the armed forces. His occupation might also suggest which of the armed forces he might have gone into if he did serve.
If he served in the armed forces his record will be held by the MOD but it will be difficult to track down his record unless you know which service he might have been in. I am not aware of any system for initiating a general inquiry across all three services, but I suppose you could try asking. Follow the process explained here:
https://www.gov.uk/get-copy-military-service-records You will need to provide as much information as possible, starting with his full name, date of birth, and possibly his address. Other things you could include are if he was married at that stage and if so, his wife's name (your grandmother, I assume). You will also need to provide a copy of his death certificate before any records, if they exist, will be released to you.
Unless something extraordinary happened to him, such as being taken prisoner of war or being declared missing for a brief period of time, there are unlikely to be any records which refer to him which are available online. That said, it would be worth putting his name into the search on sites like Ancestry, FindMyPast and Fold3 (part of Ancestry). Fortunately his surname is fairly uncommon but even so, you are likely to get a lot of false positive results which it may be difficult to eliminate.
If he is likely to have got married during the war, check the marriage certificate and it may say what his rank and service was. Also, check the electoral registers for 1946 and see if he turns up where you would expect him to be. He may well still be serving somewhere else, for instance in Europe or the Far East, and so he could listed as an absent voter, and again this should show his service details.