The problem did not just affect easyJet flights at Stansted. Other flights handled by the same handling company also had to resort to manual check-in. It is believed that the fault originated in a router that is used to link the Departure Control System (check-in) server to the rest of the airport network. Problem was fixed around lunchtime yesterday, and I believe the GLA re-routing was a result of a totally separate issue.
In the case of the passengers that were sent to LTN, I would assume that they were re-checked in there, hence the need for them to collect their bags.