There is an extensive tree on Ancestry which appears to be well-documented, but beware: you shouldn't accept anyone else's tree as being correct without careful scrutiny.
The tree is called Scrutton Family Tree - 2021 01 15 19-44 and the owner is Michael Smith.
The tree has a Cuthbert Sharp 1714-1794. He has two sons:
1) Cuthbert Sharp, 1743, m Susannah Crosby. These are the parents of Sir Cuthbert Sharp, 1781
2) Paul Sharp, 1746, m Mary Shepherd. These are the parents of another Cuthbert Sharp, 1778
Cuthbert Sharp, 1778 m Elizabeth Wilkinson and their daughter Mary Sharp, 1810 marries John Harrison, 1808. These are the parents of John Sharp Harrison, 1840.
Thus John Sharp Harrison’s grandfather (Cuthbert 1778) was the first cousin of Sir Cuthbert.