It comes as the shortage of blood test tubes has eased.
Work is now taking place to clear the backlog of non-urgent blood tests which were paused on NHS England (NHSE) guidance.
Patients who are already waiting for blood tests can now book routine appointments, but are asked to be aware that there will be an extended wait while the backlog of appointments is worked through.
For appointments at The Shrewsbury and Telford Hospital NHS Trust (SaTH) there is currently a four to six week wait for a routine blood test.
People are asked to contact the service that cancelled their previous routine appointment – either their GP practice or SaTH, to re-book their appointment.
The online booking system for blood tests carried out at SaTH has also reopened at sath.nhs.uk/bloodtests.
Patients are warned that they should not book for an urgent blood test unless their form says that it is urgent, as they might not be seen.
Blood tests for urgent health problems have continued while routine tests were paused.
NHSE has advised that the blood test tube shortage situation has eased but is not fully resolved.
Local restoration arrangements will be kept under review.