He was afterwards baptised by T. Davis of Reading, joined a Baptist church and was ordained for ministry.
He went to London, and in 1780 preached in Green Walk, on the Surrey side of Blackfriars Bridge.
Burnham published The Triumphs of Free Grace in 1787, including an account of his experience and call to the ministry.
The inscription on his gravestone is given in full in Wilson's Dissenting Churches, with an account of Burnham.
His funeral sermon, preached by William Crawford of Ewer Street, Southwark, including some account of Burnham's life, was published in 1810.