Details of the £8m proposal, which would create 120 new jobs, went on display at the Serpentine Green Shopping Centre in June to inform people about the proposal to create a 48,000 sq ft Dobbies Garden World.
Dobbies says the store will be similar to its Aberdeen centre and other new stores will have a similar blueprint.
More than 100 local people took time out to view and discuss the plans with the Dobbies team and of those that filled out a questionnaire, 97% said they backed the plans to bring a Dobbies Garden World to Hampton.
The results of the survey are revealed as Dobbies submitted its planning application to Peterborough City Council, this week.
Dobbies development manager Charlotte Swanson said: "We received a fantastic response about our proposals from local people with many telling us that they are excited about the prospect of a new garden centre on their doorstep as well as access to new jobs. The response was overwhelmingly positive and people mentioned they looked forward to the garden centre opening as soon as possible. We review all of the comments made before we submit our planning application."
The proposed Dobbies Garden World development will offer more than 10,000 plants, shrubs and trees and include outdoor areas and a specialist aquatics department within a landscaped environment.
The centre will also house a farm foodhall offering locally-grown produce from Cambridgeshire, as well as a restaurant.