When the Earl of Essex is on fire, the fire brigade arrive but there is already a fireman standing outside as the fire engine pulls to a stop. The sirens are heard in the distance, and the previous shot doesn't show any fire engines or any emergency lights that would suggest any emergency vehicles were already on scene.
When Ed is arrested he is shown in a cell. The gaoler is shown wearing Her Majesty's Prisons uniform. Later it was stated that he was released without charge; if that was the case he would have only got as far as being held in police custody, which is run by the police rather than the prison service.