A recent eMail to flight test bookings at CAA requesting approval for an examiner to carry out an initial MEIR and initial MEC on the same day was met with (swift) approval and a polite reminder that they must be carried out in two separate flights. no stipulation as to order.
As has been said already, the training has to have been completed for the MEC, but not necessarily the skills test. And that's the way we do it.