The first thing I would look for is the Hebrew names of both men. Hopefully
this will be legible >from their headstones. Otherwise the communal burial
records should contain the names of both men. If they were brothers then
they should both be named "so and so (son's name) ben (son of) Loni Peloni
(same father's name)" - with any luck the father's name will be the same.
Whilst not conclusive evidence it's certainly a start.
You could try and order their respective death certificates >from the General
Records Office to see if one of the brothers reported the other's death.
You could look at the probate records to see if either men left a Will, and
if so whether either of them referred to the other in their respective
You could see if either men naturalised by searching the records at the
National Archives. The Memorial sworn by the applicant includes details
about their parents.
If both men married in England you could apply for the marriage
certificates. This would include the name of their father. Once you have
that date, assuming they were married in an orthodox synagogue then you
could apply to the Chief Rabbi's Office for a copy of their marriage
authorisation which confirmed that the parties to the marriage was Jewish
according to Jewish law and could be married in an orthodox synagogue. This
record would provide the Hebrew name of both men (including their father's
name) and would also list the names of any brothers the groom had in case
the ceremony of "yibun" needed to be performed.
I hope this helps.
Bushey Heath, Hertfordshire