There is a reason older properties were built with Combined (or partially combined) Drainage, (mine is one, rainwater at rear goes into Combined sewer, front goes into the road, the Road Gullies are connected to a Storm sewer.)
In the early days of mains sewerage, sewage was piped to a suitable low point away from the Built up area and simply discharged into a watercourse or onto a field. (Then the next town/village downstream would be taking their water from the same watercourse to (hopefully) treat for their use!) The idea of a Combined system was in times of heavy rain, the sewers would get washed through and the land onto which the sewer drained, would get a good wash, thus allowing it to 'start again'.
Now, in normal conditions, all flow arriving at the Sewage Works is treated to a high standard before being discharged back to the environment. However, all works have a maximum flow that can be treated without overwhelming the works, so in times of heavy rainfall excess flow is diverting to holding tanks, where it is then pumped back to be treated once flows have eased. When holding tanks are full, it is permitted to discharge any further excess to the environment, bearing in mind it is diluted, and will have had chance for some of the solids to settle out first.
New builds are subject to the SuDS system, (Sustainable Drainage Systems), whereby any discharge of rainwater from the site cannot be made above the rate prior to development. Usual practices are to build Balancing Ponds, tanks or Lagoons, to contain the rainwater and release it at a controlled rate, or large soakway systems.