Up until the 1950's/60's it was accepted practice for everything to go into the same drain, usually at the rear. (Combined drainage as said.) Rainwater from the front of a lot of properties though, was often discharged into the road, whereby it found it's way into the road gullies which sometimes did connect to a storm sewer. (Partially separate system). Nowadays foul and storm drains are run independently, (Separate system).
Unfortunately though, in times of heavy rainfall, sewers become overloaded and can cause flooding, all Sewage Treatment works have a 'Storm Tank' where excess flow is collected and returned for treatment slowly once levels have dropped. If this becomes full then there is no other option than to discharge the excess flow into a watercourse. There are also various 'Combined Storm Overflows, or CSO's) around the network whereby excess storm flow from the sewers is allowed to overflow into the storm drains and away to ease pressure on the foul drainage system.