The story of these men was that they hid some stolen meat down a well behind the Rudds Arms public house and when they went to retrieve it they succumbed to the gas at the bottom. The grave inscription goes on to warn of the dangers of gas in wells.

The Stewart Park and Marton History Group was a small local history group that now, no longer meets . It had a website that was in the process of being updated with local history when the group disbanded and these are the pages that survived.
The lasting legacy of the group is the graves of Bolckow and Vaughan in Marton Churchyard, a project the group started and fund raised for and it eventually came to be, through the work of Middlesbrough Environment City.

Some additional information I have found from North East History Tour

The three men were Robert Armstrong (28), John Ingledew (39) and Joseph Fenison (28) who lost their lives on 11th October 1812.