There have been high court cases on this matter, so tread carefully!
Legally joint accounts can be held as 'joint tenants' or 'tenants in common', which determines what happens when 1 holder dies.
With state savings, joint holders are 'joint owners', and on death of one person, their name is removed from the account, and other names remain.
Court cases usually centre around showing that the 'intent' of the deceased was different to the legal status, and families fall out.