Some of the delays like that will be in the timetable, and for routine access, they can plan around it. If the Environment Agency or an ambulance needs rapid access in an emergency, they could phone the signallers and ask for the crossing to be opened.
Which means either:
-The ambulance (or whatever) still having to wait for an extended period for at least the approachign trains to pass, or
-Network Rail stomaching the delay minutes (and associated £££ in TOC compensation) by raising the barriers at the first possible opportunity whilst trains wait; which could probably form the business case to justifying a bridge replacement as best value to taxpayers.