This is doubtless a euphemistic reference to two scandals which hit the family in 1823-24:
  1. the bankruptcy of James's father, John Thurtell (1762-1846), and the consequent sale of Hobland Hall;
  2. the hanging for murder in 1824 of John Thurtell (1794-1824), son of Thomas Thurtell, who was mayor of Norwich and brother of the above bankrupt. In other words, the murderer was a first cousin (actually a double first cousin) to James (1790-1867).
A number of members of the family changed their names at this time, and James evidently took to styling himself Thurtell-Murray, and later just Murray, in order to distance himself from the scandals. Frances Jane ("Fanny", the author's great-great-grandmother) was about two to three years old at the time of these events. See details of her immediate family.