Greenhalgh's of Brandlesome

I have reason to believe that my ancestor, Robert Greenhalgh, was related to the Greenhalgh's of Brandleshome.

Robert was born in 1766 and died 15.4.1844. He married Ann Marsh (1766-1850) and they had 10 children: John (1789-1855), Thomas (1792-1828), James (1794-1842), William (1796-1855), Joseph (1799-1862), Giles (1802-1878), Ann (1805), Robert (1808-1867), Esther (1810-1878) & Mariah (1813).

Their eldest son John married Betty Walker in 1813 and their daughter Ann (1818-1900) married James Morris in 1841. They were my great-great grandparents.

Could anyone help me with a possible link to the Greenhalgh's of Brandleshome.