I visited with the Presbyterian minister, in Woolwich in 1973 to examine records of the Scots Church of Woolwich and he indicated to me that there were two historically related Presbyterian congregations in Woolwich and thus two sets of records. I notice that there are listings online for
Woolwich.
Presbyterian Church, New Road. C 1836-1920
Scots Church C 1810-1830.
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I later learned that the time when Rev. Alexander John Scott was minister, 1831-1846 was a challenge as he was not ordained by the local Presbytery due to his stand on doctrinal issues. He was well liked locally, and he remained there and preached for 15 years, and I gather this produced either a formal split with Presbyterian authorities or the roots of an eventual pair of congregations. The term Scots Church seems the older and I know that my family records from 1800 are in their record books. There is more on the life of Rev. Alexander John Scott
https://en.wikipedia.org/wiki/Alexander_John_Scott_(principal)?oldformat=trueI can find no reference to an active Presbyterian church within Woolwich currently and the final chapter of the Scots Church and New Road Presbyterian congregations appears to be covered in a local history of an ongoing Anglican church.
"In 1965, the Rev. Derek Baker and the congregation of St. Andrew’s Presbyterian Church, Woolwich came to share St Mary’s Church when their own building became unsafe. It was a case of a fully turned circle. For in 1662, the Rev. John Hawkes, the Rector of St Mary’s Church, walked out of St Mary’s to become the first Presbyterian Minister in Woolwich. St Andrew’s Church still had the bible that he had taken with him and this was re-bound to celebrate a ground breaking sharing agreement between the two churches in 1974. At first, St Andrew’s had a service each Sunday after the Anglican service, but it was soon decided to have a joint service once a month and finally it was decided to meet together every week.
In the 1970’s St Andrew’s Presbyterian Church joined the United Reformed Church, but continued to meet at St Mary’s. Sadly, due to declining numbers, St Andrew’s Church was dissolved in 2001. But good relations between our two denominations continue."
https://www.stmaryswoolwich.co.uk/page4.htmlIn the case of your duplicate records for a baptism, possibly the creation of a second Presbyterian affiliated church during the period of Rev. A. J. Scott's tenure was a factor, and that duplicate records were made as a safe guard to ensure that none of the original baptism records were ever lost, despite the fact that there would be two churches. Christian churches has typically been strict that there can never be two baptisms of the same individual so I would suggest this is either a duplicate record made by an extra cautious keeper of records so that both churches would have a record for posterity or possibly two individuals with the same name. Good luck with your research.