Lucy Allan, MP for Telford, and Mark Pritchard, MP for The Wrekin, have sent their request to Sir Neil McKay, the chair of the Shropshire and Telford & Wrekin Sustainability and Transformation Partnership – the organisation responsible for the future of healthcare in the county.
The Future Fit plan, which was finally agreed in 2019 after years of discussions, would see Royal Shrewsbury Hospital (RSH) become home to the county's only 24-hour A&E.
Consultant-led women and children's services would also move from Telford to Shrewsbury, with Princess Royal Hospital Telford (PRH) becoming a centre for planned care.
Mrs Allan and Mr Pritchard say the review is required because the "post-pandemic landscape" will "bring about fundamental change in both healthcare delivery and healthcare need".
The letter also says the new management at Shrewsbury & Telford Hospital NHS Trust (SatH), which manages PRH and RSH, will have to put their names to a plan they did not devise.
It states: "There has been a significant senior leadership shake-up at both SaTH and the county's clinical commissioning group.
"The decision makers will need to take ownership of these proposals and be held account for the decisions made.
"The current management will be required to make the case for and defend a highly controversial plan that they have had no part in approving or developing and may well not support."
Both Mr Pritchard and Mrs Allan said that the level of local opposition in Telford & Wrekin, and the increase in costs for the project – when set against the background of the pandemic – mean they believe a rethink is required.
Their letter states: "Such significant investment into the county's healthcare infrastructure must reflect current challenges and current healthcare needs and priorities.
"There is very significant opposition to the proposal from our constituents and all local elected representatives.
"The Future Fit proposal was first developed in 2014. We contend that it must be reviewed and updated to make it relevant to 2021 and beyond.
"There has also been an exponential rise in the projected cost of Future Fit, including capital build inflation as well as other rising costs, from an initial estimate of £312 million up to the current forecasted cost of £498 million.
"Failure to review Future Fit in light of such a fundamental change will further undermine the proposal."