Can I assume that you have Jack's naturalisation papers from Kew, which is also online?
According to the census,whee they always in London? have you looked at 1939 register? Also on the census pages you will often find family living either with them, or nearby.
RAYKH-ZELIGMAN/RICHMAN, Stakliskes, Lithuania/Leeds
COHEN, Sakiai, Lithuania/Leeds
MAGIDOWITZ, Jurbarkas, Lithuania/Leeds
KASSIMOFF, Rezekne, Latvia/Leeds
MULVIDSON, Rezekne, Latvia/Sweden
GREENSTONE, Rezekne, Latvia/Leeds
ITMAN, Stakliskes, Lithuania/USA
KANTOR, Sakiai, Lithuania
GOLDBERG, Sakiai, Lithuania