Robert Kelham was an English attorney and legal antiquary.
He was the son of Robert Kelham, vicar of Billingborough, Threckingham, and Walcot, in Lincolnshire.
He practised as an attorney in the Court of King"s Bench until 1792. He died at Bush Hill, Edmonton on 29 March 1808, in his ninety-first year, and was buried at Saint Michael Royal, College Hill, London. Kelham married Sarah, youngest daughter of Peter and Joanna Gery, of the family of Gery of Bilstone, Leicestershire.