Mum and Dad applied to emmigrate from the UK to Australia, but they got worried because:
1. A person Dad knew in Melbourne offered to sponsor them, but Dad was unable to get in contact with them.
2. Dad had trouble tracking down his birth certificate.
3. They had changed address from Grandma's place to a house of their own, and thought maybe correspondence from Australian Migration might have been lost.
This delayed their application, and I imagine they thought they might have blown their chances of migrating.
Incidentally, mum wrote the letter, but Dad signed it. That's definately mum's handwriting.
Interesting note: Mum sent the letter on 20 Aug 1963, and Australian Migration received it on 21 August, the next day. The British post service was pretty efficient in 1963!