The new facility will involve work on future "biological warfare" dangers says the government.
MP John Glen says moving the agency to Harlow does not recognise "Porton Down's existing expertise".
The government wants to invest billions to make the National Biosecurity Centre the largest in Europe.
Salisbury MP John Glen asked the chancellor for an update, only to be told it was the Health Secretary's decision.
Government spending review to include a decision on if the labs in Wiltshire will move to Essex.
A new team at Porton Down will improve the speed that tests can be made for new diseases.
The MoD says a section of Winterslow Road will be closed during the day for "operation reasons."
Costs have skyrocketed from £530m to more than £3bn and it is set to open 15 years late in 2036.
The defence secretary said the laser could be used to take down Russian drones as early as 2027.
