There were a few questions about bankruptcy after my talk, and I just wanted to pop a few links in a post for anybody wishing to research the topic. I am certainly not a specialist in this area, but hopefully, these are good places to start if you would like to learn more:
As is very often the case, the National Archives has an excellent research guide.
Newspapers, including the London Gazette, can sometimes flesh out the story. So try lots of search terms there and at the British Newspaper Archive, The Times and other standalone newspaper archive services (many of which may be available for free through your local library).
There may be surviving records held locally at County Record Offices or in possession of former directors. That said, please tread extremely carefully if you want to view sensitive material held in personal archives of living people or businesses!
Court records/case papers sometimes survive at TNA or in local archives, but it is difficult to generalise as survival and accessibility differ over time and across geographical boundaries. I’d recommend looking for guides on websites or contacting your local repositories to see what they might have and, of course, searching their catalogues by business and personal names.
Very often, people that went bankrupt were quickly back in business! For more on the legislative changes to the business environment, see this additional TNA research guide.
I hope that helps!