You can try various search combinations on the NA advanced search page to cross check what you've been told already.
http://discovery.nationalarchives.gov.uk/advanced-search using combinations of Malta or Maltese and putting WO (for army records) or ADM (for RN records) in the References box and using the dates boxes to limit the dates. However, those army records that did survive the second war, and the extant RN records are on Ancestry or Findmypast and I, and others, are using those to answer your queries.
This NA guide is very useful
http://www.nationalarchives.gov.uk/pathways/firstworldwar/service_records/sr_soldiers.htmA sample search on "Malta" and "service" with WO throws up 600 odd medal cards (all of which could also be found by name) and a few officers records but no soldiers records. The same search on ADM throws up 188 mostly medal records and some service records, again all of which are searchable by name.
Among these are of course the ones for the names you have given already. Significant though is that if someone did not serve in a war theatre, then there would be no medal card and if that same person's record has not survived than that means no trace at all.
Doesn't help much I'm afraid. If you have other names/dates of birth start a new thread for each and keep plugging away!
maxD
Birkbeck - yes. that is the same name V Brincat (number 3862 Maltese Labour Corps) but the poster gave the service number 10523 and the discharge date is wrong so I mentioned him just to discount him.