Just letting my imagination go haywire.
It is more than likley that they anglicized their surnames after arriving in Britain and looking for Boodson in Russia will lead to nothing
Possible surnames could have been:
Bodzon, Bodzyn, Bodzen or Budzon, Budzyn, Budzen
If you search in Ancestry and Family Search for Bodzon/Budzin you get results that lead to places like:
Braslaw, Poland
Aleksandrow, Poland
Lodz, Poland
Tuchel (Tuchola), Poland
Suwalken, Poland/Russia
Zygmuntowo, Poland/Russia
A lot of jewish familys came from Suwlaken, Polish - Russian border area
https://www.jewishgen.org/Yizkor/Suwalki/suwe009.htmlI didnīt find any hits that fit your query, this is all very speculative and it could be a load of nonsense, but i think it could be worth given a thought.
Dave