One of the criminals being hanged is announced as one "James Saville", a rather obvious allusion to real-life (in)famous British TV programs presenter, Jimmy Savile (complete with his trademark long white hair and all) who, after his death in 2011, was found to have sexually abused dozens of children in his lifetime.
Peggy mentions stopping off for a meal at a Happy Eater. This was a road side restaurant chain that first opened in 1973. Due to a decline in the 1990's they eventually all closed down by 1997. Additionally, a Happy Eater was never located "just past Luton".
For the record: In the real world, public executions in the UK were abolished in 1868. So, obviously, no such event would ever have been televised, underlining even further how _not_ historically accurate the show sets itself out to be.