Whitehall Medical Practice in Monkmoor will close at the end of September when the current contract with Malling Health ends.
Shropshire Clinical Commissioning Group (CCG) has been unable to find a new provider, leaving about 3,700 patients to find a new GP.
Dennis Cheese, patient and organiser of a petition to save the practice, Phil Batho, chairman of the patients' group and Councillor David Vasmer have now written to Shrewsbury MP Daniel Kawczynski.
The letter thanked Mr Kawczynski for writing to the CCG objecting the closure, but added that they feel he could take further action.
"Could you raise the issue in parliament in a written or oral question?," the letter said.
"Or perhaps sponsor a debate? When we took our objections to the closure of the Whitehall Practice to a Shropshire scrutiny committee, we were amazed to discover that there is a lot of frustration among many councillors with the actions of the Shropshire CCG -some from your own party. Could that be the case amongst some MPs with their own CCGs?"
The letter also invited Mr Kawczynski to a public meeting on September 9 at Crowmoor Baptist Church.
It added: "One of the issues that is coming to the fore now is the problems many Whitehall patients are having registering with other practices. Despite assurances from the CCG, we believe that some people could be left without being registered with a practice after Whitehall closes on September 27.
"At our last public meeting patients registered with other GP practices in Shrewsbury raised their concern about the impact that an influx of patients from Whitehall could have on the services at their own very busy practices - a problem that will be compounded by the growing number of new residents in housing developments like Weir Hill who will also be looking to register with an existing GP Practice.
"Waiting times for a GP appointment are not as bad as in other parts of the country at the moment but, with the closure of Whitehall and the town’s rapidly growing population, waiting times could climb quickly."