Dawn Sturgess, 44, fell ill in Amesbury months after the incident and died in hospital in July after coming into contact with a perfume bottle believed to have been used in the attack on the Skripals and then discarded.
Her partner, Charlie Rowley, 45, was also exposed to the same nerve agent but was treated and discharged.
In this latest phase of operation, the roofs on two buildings will be taken off during a two-week period with other areas also being removed.
A letter seen by the Press Association and signed by the council's director of public of health, Tracy Daszkiewicz, told residents that contractors would spend the first month erecting scaffolding to cover the house and garage with a "sealed frame". She added:
"All materials will be wrapped and sealed on site before being removed safely from the premises."
She said the risk to public health remains "low".
Wiltshire Council has written to the Skripal's neighbours to say the deep clean and construction work is expected to take up to four months in total.