It is anticipated that construction work will begin in 2023 and finish in 2028, although the department warns "any change in scope could require further consultation" which would affect the timetable.
The Future Fit project, which has already incurred costs of more than £4m, has secured £312m from the Government but costs for delivering the full scheme have risen to more than £530m – mostly due to inflation.
It comes after Shrewsbury MP Daniel Kawczynski called for the National Audit Office (NAO) to investigate the cost to the taxpayer of delays to the scheme, which will see the 24-hour emergency unit at Telford's Princess Royal Hospital downgraded to a part-time 'A & E local' centre.
It will also see consultant-led women-and-children services move to Shrewsbury, while PRH will be used for planned care.
In a letter to Mr Kawczynski, comptroller and auditor general Gareth Davies, from the NAO, said there are a number of elements of the programme for which no budget has yet been approved.
He wrote: "It is not clear at this stage whether or how an increase in costs could be funded.
"If additional funding is not secured, the proposal may have to be descoped to make it affordable within the £312 million funding approved to date.
"Any change in scope could require further consultation and could affect the timetable for works completing.
"The programme incurred costs of £1.46 million up to the end of March 2019, and the trust incurred an additional £2.63 million of related costs in the period from April 2016 to April 2021.
"There remain uncertainties. Until these are resolved, our view is that the target completion date of summer 2028 should be viewed as provisional and liable to change."
He said the office's review had identified two significant factors behind delays to the scheme so far – the first was the challenge of securing agreement from two clinical commissioning groups.
The second factor was the strength of feeling expressed in consultations, leading to several independent reviews of the programme and "may have created additional delays through the need to respond to the volume of comments", Mr Davies writes.
He added: "It is not clear to us whether anything could have been done to shorten the time taken or whether the original timetable would always have been at risk."
However, at a meeting of Telford & Wrekin Council's health and wellbeing board on Thursday, Shropshire, Telford & Wrekin CCG's interim accountable officer Claire Skidmore said the increased costs needed to be addressed, but there was “no intention to deviate” from the approved plan.
The Shrewsbury and Telford Hospital NHS Trust, which runs PRH and Royal Shrewsbury Hospital, said the initial business case for the project is expected to be complete by the end of July.