In <em>The Baptist Story</em>, Michael Haykin describes how in 1644 Mark Lucar came from London and joined John Clarke and the Newport Baptists, and shortly after the group adopted immersion as the mode of believer's baptism. Perhaps if you dig around you could find the letters of Lucar or Clarke, or maybe the minutes of that congregation if we have them.
If you want an alternate view I would suggest that you read "The Baptist Story" by Haykin, Chute, and Finn. https://www.amazon.com/Baptist-Story-English-Global-Movement/dp/1433673754
The Baptist Story: From English Sect to Global Movement is decent if you want a less USA centered version of history. Preview here
for a more american view - browse here