Hi Alex,
That's good. With military records once you supply the information it is pretty much a waiting game and they are quite busy.
With MN enquiries, there will be some work to do and probably a little cost as you have to provide the evidence of service [proof of ships he was aboard and where they were operating]. The application form will be submitted by his actual next-of-kin. You have some documents already but they are not enough, they are quite strict on what is required. Some of the information that you do not already have can be obtained for free such as MN Movement Cards for the ships he served in for the qualifying period.
What should you do first?
Contact the Registry of Shipping and Seamen (RSS) at Cardiff and ask them if they have a medal entitlement for 'Peter Smart Balfour, R118760 b. 25.1.1905, d. 2.11.1941'.
They may already have a medal entitlement for him, if so, great but I cannot see one online for him in the database. If they don't have an entitlement they will send you an application form with information on what you require to obtain. It is not an easy journey but I can guide you with it. So do that first.
Registry of Shipping and Seamen
MCA, Cardiff
Anchor Court
Ocean Way
Cardiff CF24 5JW
Tel: 02920 448800
Email: seafarers_registry@mcga.gov.uk
Website: Maritime and Coastguard Agency - GOV.UK
Regards
Hugh