For the sake of folks looking for Rogers in the future I'll summarise what I've found
Andrew's John 1755-1829 was probably from Bourn, Cambs. His father, also John Rogers, had 19 children by two wives, in Bourn Cambs, and Biggleswade and Southill, Beds. The family looks something like this:
I. John ROGERS was born circa 1733. He married Rachel NEWNHAM or NEWMAN on 22 Jul 1754 at Bourn, Cambs. He married Elizabeth DARLOW, daughter of Thomas DARLOW and Susannah (--?--), on 20 Sep 1773 at Bourn, Cambs. He appeared on the census of 1801 at Broom, Southill, Beds. He died in Feb 1806 at Bourn, Cambs. He was buried on 24 Feb 1806 at Bourn, Cambs, age 73.
A. John ROGERS was christened on 17 Aug 1755 at Bourn, Cambs. He married Elizabeth WHITE on 9 Nov 1778 at Croydon cum Clapton, Cambs. He married Jane CRAWLEY on 30 Oct 1794 at Potton, Beds. In his will dated 31 May 1828 bequests were made to his grandchildren John, Elizabeth, and Jane Rogers, children of his late son James; his son John Rogers of Cambridge; to Jemima Rogers of Baldock, the widow of his late son William; to Mary Rogers, now living with him; his sister Ann Page, widow; his mother in law (=step mother) Elizabeth Rogers, widow. Executors son John and grandson John. He died in Dec 1829 at Potton,
Beds. He was buried on 13 Dec 1829 at Potton, Beds, age 75.
1. William ROGERS was christened on 28 Aug 1779 at Potton, Beds. He married Jemima BARBER on 2 Mar 1802 at Potton, Beds. He died before May 1828.
2. Catharine ROGERS was christened on 21 Mar 1781 at Potton, Beds. She died in Apr 1805 at Potton, Beds. She, age 24, was buried on 25 Apr 1805 at Potton, Beds.
3. John ROGERS was christened on 11 Jun 1783 at Potton, Beds. He
married Ann THOMPSON on 31 Jan 1803 at St Edward, Cambridge.
4. Elizabeth ROGERS was christened on 5 Apr 1785 at Potton, Beds.
She died in Dec 1786 at Potton, Beds. She, infant, was buried on 28 Dec 1786 at Potton, Beds.
5. James ROGERS was christened on 11 Feb 1788 at Potton, Beds. He married Mary MEEKS on 15 Jun 1812 at Potton, Beds. He died in Jul 1819 at Potton, Beds. He, age 31, was buried on 25 Jul 1819 at Potton, Beds.
6. Elizabeth ROGERS was christened on 14 Jun 1790 at Potton, Beds. She died in Jul 1802 at Potton, Beds. She, age 13, was buried on 14 Jul 1802 at Potton, Beds.
7. Thomas ROGERS was christened on 2 Jun 1792 at Potton, Beds. He died in Apr 1802 at Potton, Beds. He, age 10, was buried on 16 Apr 1802 at Potton, Beds.
B. Robert ROGERS was christened on 29 Aug 1756 at Bourn, Cambs. He died in Jun 1766 at Kingston, Cambs. He was buried on 18 Jun 1766 at Bourn, Cambs.
C. Newman ROGERS was christened on 14 May 1758 at Bourn, Cambs. He died in Mar 1767 at Kingston, Cambs. He was buried on 21 Mar 1767 at Bourn, Cambs.
D. Sarah ROGERS was christened on 8 Jun 1760 at Bourn, Cambs. She died in Nov 1761 at Bourn, Cambs. She was buried on 15 Nov 1761 at Bourn, Cambs.
E. Alice ROGERS was christened on 16 May 1762 at Bourn, Cambs. She was buried on 30 Nov 1775 at Bourn, Cambs.
F. Gregory ROGERS was christened on 8 Jan 1764 at Bourn, Cambs.
G. Rachel ROGERS was born on 22 Dec 1765 at Bourn, Cambs.
H. Sarah ROGERS was christened on 20 Mar 1768 at Kingston, Cambs.
I. Ann ROGERS was christened on 30 Apr 1770 at Kingston, Cambs.
J. Elizabeth ROGERS. She was christened on 28 Dec 1777 at Bourn,
Cambs. She married Joseph CHEW on 31 Jul 1797 at Southill, Beds. She married William SAYWELL on 30 Dec 1818 at Bourn, Cambs.
1. Joseph CHEW was christened on 21 Jul 1799 at Southill,
Beds. He married Susannah TRIPLOW on 12 Oct 1818 at
Bassingbourn, Cambs.
2. Elizabeth CHEW was christened on 21 Jul 1799 at Southill
3. John CHEW was born on 7 Jul 1805 at Bourn, Cambs.
Illegitimate
4. Catherine CHEW was christened on 14 May 1807 at Bourn,
Cambs. Illeg.
5. William CHEW was also known as SAYWELL. He was christened
on 12 Jul 1812 at Bourn, Cambs. Illegitimate
6. Jane CHEW was christened on 12 Jun 1814 at Bourn, Cambs.
Illegitimate
7. Rachel SAYWELL was born in 1821 at Bourn, Cambs. She
married David CHAPMAN on 25 Dec 1847 at Bourn, Cambs.
Continued