I am researching my family tree and i have a Phillip Acton born abt 1756, around the time you are interested in, he had children called: John Acton (1778-). William Acton (1779-1840). Ann Acton (1781-). Sarah Acton (1783-1819). Philip Acton (1787-). Richard Acton (1791-). Joseph Acton of Macclesfield (1793-1878 Thomas Acton (1780-1811). Theodosia Acton (1796-1821).
Your John could be a child of of one of these.I am linked in through William and he did not have a son John as far as i know so far.