Filming for Stonehouse will take place in Clarendon Square between February 4 to 8.
John Stonehouse was a British Labour and Co-operative Party politician and cabinet minister under Prime Minister Harold Wilson who is remembered for his unsuccessful attempt at faking his own death in 1974.
The series will tell the story of the life and times of John Stonehouse and of the scandal he was involved in during the 1960s and 1970s, which led to him taking such drastic action.
Residents have received letters giving them notice of the filming by production company Snowed-In Productions.
In the letter, the company's location manager Matthew Venables has told residents that the film crew will try to reduce the disruption and inconvenience to them.
Mr Venables said: "Preparation works are already underway and residents will notice an increase in activity in the area in the coming days and weeks.
"We do have some exterior scenes [to film] - currently scheduled for Tuesday February 2 - and being a period show we would be seeking to exercise a degree of control when shooting these.
"As you'd expect, we'd very much like to avoid any embarrassing mistakes in the form of modern inclusions.
"For this work to be successful I will propose a plan that will be reliant on your help and support."
Mr Venables will contact residents again in the coming days with more details about the plan.