You did not write if you have exhausted absolutely all possible sources of information available to you in England.
For example, what is “Jewish community”? A synagogue? Which one? Have you inquired if they had any records of interest to you?
Have you checked published sources, e.g. newspapers? There may be a 25 words news piece.
What is “taught a trade”? Which trade? Who taught? There may be a paper trail there.
Without knowing anything else about the family location, a reasonable assumption is that it would be Latvia (i.e. Courland) rather than Lithuania. However, Cossacks did not operated in Courland. They were a scourge in Russia and Ukraine. That is until World War I, when there were everywhere, as a part of the Russian Army. (butu you did not write the year your grandfather came to the UK).
FAST Genealogy Service