Years ago, I once owned a copy of the aforementioned painting given to me by James A. Dickson after a rather large book purchase at his Christian bookstore, but later sold it after I learned more about the picture.
The story behind the picture can be found in a review by The Baptist Magazine for 1849, published by the Baptist Missionary Society, Vol. XLI, pp. 494-498.
The painting is by J.R. Herbert [John Rogers Herbert, 1810 - 1890, converted to Roman Catholicism in 1840] (engraved by Samuel Bellin, published by Thomas Agnew) and was first published on December 16, 1848 (first displayed, perhaps, in 1847). It is entitled "Assertion of Liberty of Conscience by the Independents in the Westminster Assembly of Divines, 1644." It shows Philip Nye arguing against Presbyterianism in that it was unfavorable to civil liberty. The prospectus that accompanied the publication of this painting makes unsubstantianted claims about Philip Nye's specific words, but the gist of it is that the painting purports to show the Independent's argument against Presbyterianism, with a revisionist or poetic attempt to show Oliver Cromwell, John Owen and John Milton in attendance, none of whom are known to have actually been present.
It's a beautiful picture which glorifies the Independents in the Westminster Assembly, while containing a number of historical inaccuracies (acknowledged and decried in the Baptist article referenced above).
That, in a nutshell, is the story behind the picture.