An idea About the Thames Tideway Tunnel

The summary is that yes, it's a net win. If you build a new city today (and indeed when new cities were built in the mid 20th century onward) combined sewers are not normally used. Rain water from gutters and pavements flows into storm sewers and both the "black water" (human waste) and "grey water" (washing machines, baths, etc.) go into the sanitary sewers which lead to a treatment plant.

In principle "separating" London's sewers isn't impossible. But it would be prohibitively expensive. Some US cities have done it, but we're not talking about New York or Los Angeles here, but rather places like Minneapolis - scarcely comparable to London in either size or density.