Here's an update for everyone - I received a birth certificate today of one of the children in this family and it turns out that my mother in law's parents
were married - at the end of 1939

Looks like when war broke out they decided to become legitimate lol
The upshot of this is that I have now found a reference to their marriage certificate which I can now send off for and find out who the paternal grandparents were

Thank you everyone. This line of inquiry was
very worth pursuing
