Needham was the son of John Needham, Baptist minister of Hitchin, Hertfordshire, England.
He was doubtless educated by his father, who was a tutor and in repute as a learned man.
In 1746, Needham moved to Bristol, where in 1750 he became co-pastor with John Beddome at the Baptist meeting house in Pithay. Two years later, Beddome having retired, a violent controversy arose within the church regarding the co-pastor system.
As a result, Needham and a number of his friends moved to a Baptist meeting house in Callowhill Street, where a Mr. Foot was pastor. For a time the two groups used the same building at different hours, but in 1755 they united, with Needham and Foot as co-pastors. The arrangement continued at least to 1774, but both Needham and Foot died by 1787.
I Come,the Great Redeemer Cries
’Tis Finished,the Redeemer Cries