They asked for a meeting to discuss the "rationale" behind the decision, particularly at a time when they said Hounslow has "an exciting future ahead".
"Marks and Spencer has always been a valued part of our community. We very much wish to see you stay, or hope that you will engage in discussion and consider a return in the future," they concluded.
The retailer announced on Monday (June 22), that it had started consultation over the closure of its branch in High Street, Hounslow.
The store, which has 60 staff, is one of four M&S Outlet discount shops nationwide facing the axe.
Ms Cadbury, Labour MP for Brentford & Isleworth, said: "Hounslow High Street has been on the up recently, with new stores such as H&M and Topshop opening. That's why this announcement is such a shock.
"The area is set to grow with the new development that is under way, which I was proud to have led on during my time on the council, and M&S should want to be part of that future.
"I urge them to reconsider, perhaps to even take some space in the new shopping area that will open in a few years."
Ms Malhotra, Labour MP for Feltham & Heston, said: "The whole community will be saddened by the news that a landmark store like M&S has taken the decision to leave just as Hounslow moves forward into an exciting new phase of development.
"I believe this move sends the wrong message about Hounslow as a place to live, work and invest. The story of M&S in Britain has been of entrepreneurship, innovation and community service.
"This store is where my sister had her first job. I hope that we can send a message to M&S that we hope even at this late stage they can reconsider this decision."