Fulham Old & New
In looking for the oldest record in the Bower Family Tree, I returned to the text in the book Fulham Old & New:
The oldest record is of George Bower operating a smallholding at Rowberry Mead, near Fulham Parish Church alongside the Thames towpath, in 1757:
His son William (1795) and his wife Elizabeth (1823) later resided there.
There was an article in the Gentleman's Magazine that may be applicable:
Gentleman's Magazine Dec 1764
Bankrupts
William Bower of Fulham, Gardener
Land Tax Records
There is also an entry in Land Tax Records:
UK, Land Tax Redemption 1798
Proprietor - Executors of Mr Cobb
Tenant - Wm Bower
There are similar entries in 1799 & 1802 for the Executors of Wm Cobb.