They didn't direct some of the rainwater into the sewer, it was all directed in and storm overflows incorporated at strategic points in the system to send excess to rivers etc.
In my area, we have various Victorian streets, where the rainwater from the rear of the properties goes into the combined sewer. All runoff from roofs at the front is directed into the road, where the road Gullies are connected to a separate storm drain. There are several CSO's dotted around the town, but these are all recent additions in the last 50 odd years, to ease surcharging on the older parts of the system, which have become under increased pressure as the town has expanded.
Treatment Works also have Storm Tanks to contain excess flows during wet weather and retain as much effluent as possible to return for treatment as incoming flows subside.