Bradford Estates was responding to concerns raised by residents and Tong Parish Council about the use of Hubbal Lane.
Claims have been made that houses "shake" from passing lorries, which travel by as early as 5am.
The planning application seeks to legitimise a change of use of barns at Tong Hill Farm, allowing the company Hire This to continue to store and refurbish portable site accommodation.
Alexander Newport, managing director of Bradford Estates, said: "We appreciate the concerns raised by Tong Parish Council and one of our local residents around traffic movements on Hubbal Lane. As the Estates’ management team, our intention is always to be responsible and responsive, and enter into positive dialogue wherever possible.
"The farm has recently been taken back in hand from a tenant farmer, who had sub-let the farm for commercial use without having the proper planning permissions in place.
"Our subsequent change of use applications have been sought to regularise the use of the site, allowing us to put in place proper measures to limit the hours of use and the number of traffic movements to and from the site for the benefit of the local community.
“As the bulk of the farm has now been given consent for change of use by Shropshire Council, we are now hoping to finalise the change of use for the remaining part of the farm used by a local storage company, whose vehicles currently accessing the site are of a similar size to modern-day tractors presently permitted under agricultural use.”
Shropshire Council's planning committee is set to decide on the application at an upcoming meeting.