The Particulars did not come later. The 1640 theory has been totally disproven by J.T. Christian. Both Kiffin and Knollys claimed that the churches in London had been organized by Preachers coming from early churches in the country side outside of London:
"I say that I know by mine own experience (having walked with them) that they were thus gathered; Viz., Some godly and learned men of approved gifts and abilities for the ministry, BEING DRIVEN OUT OF THE COUNTRIES where they lived by the persecution of the Prelates [Episcopalians] came to sojourn in this great city....." - Hensard Knollys - A Moderate Answer Unto Dr. Bastwick's Book Called Independency not God's Ordinance. London, 1645
"It is well known to many and especially to ourselves that our congregations as they are now, were erected and framed according to the rule of Christ BEFORE WE HEARD OF ANY REFORMATION EVEN AT THE TIME WHEN EPISOPACY WAS AT THE HEIGHT OF ITS VANISHING GLORY." - William Kiffin: A Brief Response of the Reasons of those People Called Anabaptists for their Separation; London, 1645, p. 6
Dr. John T. Christian researched this quotation and found that a Mr. Joseph Richart, who corresponded with Kiffin over this statement said:
Mr. Joseph Richart, who says he wrote the queries to which Kiffin replied, affirmed tht he understood the Episcopal and not the Presbyterian Reformation. "You allege," he says, "your practice, that your congreations were errected and framed in the time of the Episcopacy, and before you heard of any Reformation." (Richart, A Looking Glass For Anabaptists, p. 7 London 1645).
Here were Baptists churches, according to Kiffin, before the times of Henry VIII. And this fact was well known to the Baptists. Further on Kiffin makes the claim that the Baptists outdated the Presbyterians. - John T. Christian, A History of the Baptists, Vol. 2, p. 255
The Church in the Hop Garden can be dated by archeological remains to as early as 1414 (John Stanely, The Church in the Hop Garden) and the Hillcliffe Baptist church as early as 1300's based upon archeological remains.