Unfortnately having a British grandparent doesn't make you British or eligible to Dual Citizenship. It is dependent on what your parent(s) citizenship is.
Where were your parents born?
Were they married at the time of your birth?
Where & what year were you born?
However, with a British Grandparent & if you were born in the Commonwealth you may qualify for an
Ancestry visa, but I do believe that it still carries the 'no public funds' clause.