A specialist team has begun a ninth day of excavations close to where the 21-month-old went missing in 1991.
Detective Inspector Jon Cousins told reporters his negotiations with the farmhouse owners were successful but he acknowledged it was a difficult decision for them.
The officer thanked the family for their understanding.
He said on Tuesday: “Discussions I’ve had with the family that own the farmhouse have resulted in the fact that at some stage early afternoon I will be dismantling the lower part of the farmhouse and clearing the ground around it - as I said before, just making sure that I haven’t missed any opportunities to get the answers that we require.”
Mr Cousins said a newspaper photograph from 1991 had alerted the team to the fact that the extension he is to demolish was not there when Ben disappeared.
He added that it will be up to the family whether it is rebuilt but he confirmed that was not the plan at the moment.
Mr Cousins said: “The family are clearly upset about what we’re doing.
“They have very kindly agreed to allow us to do that and I am extremely grateful for that.
“Clearly it’s going to be a distressing time for them. This is where many generations, including the current generation, were born and grew up and we’ve got to deal with it as sensitively as possible.”
The excavation began after new evidence was found that Ben, from Sheffield, may have been killed and buried there, yards from where he vanished while his grandfather was renovating the property.
A 19-strong team from South Yorkshire Police was sent to the island to investigate claims that the toddler might have been killed by a digger driver working on the 2.5-acre site.
Ben’s mother, Kerry Needham, had been warned to “prepare for the worst”.
Konstantinos Barkas, also known as Dino, was clearing land with an excavator close to where the youngster was playing on the day he vanished and may be responsible for his death, a friend of the builder reportedly told police following a TV appeal in May.
The driver reportedly died of stomach cancer last year.