I've just been searching for what you have on the Birmingham Political Union, and found this thread. In belated answer to Tinpot's question:
I have that same picture in my copy of the
The Collected Essays of Asa Briggs, captioned
"The Gathering of the Unions" on New Hall Hill, 7 May 1832. This turns out to be an engraving by Henry Harris ("Drawn on Stone from Sketches taken during the Three succeſsive Meetings in May 1832"), of which various prints exist. The British Museum have a copy, as do the Working Class Movement Library in Salford and others, though I can't tell if it's currently on display anywhere.
www.wcml.org.uk
The Benjamin Haydon oil painting is perhaps this one:
(from
https://en.wikipedia.org/wiki/Birmingham_Political_Union)
The source below relates that Haydon was unable to raise the subscription for the full work, so only the above sketch was completed. It shows the Rev. Hugh Hutton leading the opening prayers on the meeting of 16 May 1832, celebrating the recall of Earl Grey as Prime Minister, with Thomas Attwood at the reverend's side preparing to address the crowd.
https://www.barricades.ac.uk/items/show/71
It sounds like Birmingham Museum has the original.