Hi
FreeBMD is only transcribed up to about 1930 so is probably not much help; and we do not know if Josef's older children were born in this country or even if he married here.
There were at least 46 Babics born here between 1929-1969 and 16 Babic marriages.
It is just as likely that Josef arrived in the UK between wars or after WW2.
Geneanet seems to be a predominently French site - try putting JONES in and see what results come up

Babic does sound eastern European, it just doesn't sound very Polish; for example in the Poznan Project, which indexes marriages in the Poznan region which consisted of around 10 million people at the end of the 19th century and covers the period 1835-1884, there is only one exact match for Babic; the nearest
most common variant is Babiak.
http://genealogy.familyeducation.com/surname-origin/babicThe above site gives the origin as Serbo-Croatian, Slovenian, Czech and Slovak.
http://www.croatian-genealogy.com/cro-surnames/03-babic.shtmlThe above site says that Babic is the third most frequent surname found in Croatia.
Just throwing some food for thought into the pot

Kind regards
Gaie