I don't know about elsewhere, but here in Ireland pedestrianised streets are usually open to deliveries in the early hours of the morning. I think they open to one-way traffic some time after the pubs and clubs close, and late-night foot traffic is reduced. Then the bollards go up at the entrance end at around 7am, and go up at the exit a little later.

Certainly I've seen delivery vehicles on Grafton Street in Dublin and Shop Street in Galway in the early hours.