'... ordinary lay people didn't normally go into the choir of a cathedral or a monastery ... '
Let’s go back into the nave through the Monks' Door. In the Middle Ages, we would now have been to the east of the pulpitum screen and in the monks’ part of the church. Turning right (east) from the Monks’ Door, we come into the south transept.
The transepts, or cross-arms, of the church helped to stabilise the central tower over the crossing by providing lateral thrust against it. They also provided space for extra chapels.
In the Middle Ages, ordinary lay people didn’t normally go into the choir of a cathedral or monastery, but many pilgrims wanted to visit the shrine of St Etheldreda in Ely’s choir. So a special entrance was made for them in the north transept. None the less, access to the shrine was probably quite strictly controlled, rather like going on a modern-day guided tour.
At Ely the transepts are the oldest surviving part of the cathedral. In anglo-Norman times, great churches were built from east to west, so that the choir could be used while the nave was still under construction. Ely’s Romanesque choir would, therefore, have been built before the transepts, but the choir was rebuilt after the crossing tower fell in 1322.