As I understand it, the high mileage children were those in the diplomatic and military, or whose parents were ex-pats in HKG, SIN and so forth. The children might be at school in the UK and go out and back every year, or more.
If you have time to waste (which I didn't but I wasted it anyway ...
)
Search eBay co uk for 'Junior Jet Club'
Search also in your regular search engine. Quite apart from the expected results, there are some mixed up ones of music and other stuff.
I also learnt that the JJC was formed in 26th March 1957! and the enthusiast that runs a VC-10 web site has this:
Testing and early days
Oh well, I had better go and see my clients and leave childhood behind for a while ...