There's nothing stupid about it, and since he was in the Royal Army Medical Corps, and since Catterick was a garrison town, it seems reasonable that accommodation would have been provided in the military hospital or in it's grounds, but he might just have meant that as being his unit as opposed to his actual accommodation.
You can get his service record from the Ministry of Defence, but you will need his death certificate and his date of birth.https://www.gov.uk/government/organisations/ministry-of-defe...https://www.gov.uk/requests-for-personal-data-and-service-re...http://www.gro.gov.uk/gro/content/
With his age and or place of birth his parentage can be found.
Post that info if you know it and you want to.
If he was born in Northern or Southern Ireland you can get his long version birth certificate from below.https://www.gov.uk/general-register-office-for-northern-irel...http://www.groireland.ie/
Ah, I've just seen that you said elsewhere that he was born in Longford.
You're doing the right thing by getting his marriage certificate.
Don't faff around with genealogical sites for Irish birth events nor with whatever that Irish certificate site was that someone mentioned to you.
You want groirireland, that's the official Irish government registration organisation
You also said that he came to England to do his National Service, well Irish citizens have no obligation of loyalty to the British Crown, because they're not British subjects so he couldn't have been conscripted during the era of national service, he must have enlisted voluntarily, and you can bet that he had to produce proof of his age and next of kin.
Another point, WW2 identity cards were still in use in Britain up until February 1952, and you can get a copy of that information.http://www.1911census.org.uk/1939.htmhttp://www.hscic.gov.uk/register-service
Because he was born in Ireland, that means that his children and his grandchildren, even if they were born in Britain, are also Irish citizens.
So, you have dual nationality, in other words, you are a citizen of the Republic of Ireland, i.e. you are Irish, and if you want to you can have an Irish passport.