My city is being pushed into doing this and we can't afford to upgrade to a newer vehicle before it arrives. Whilst we walk where possible, for bulky items (such as the tip run, IKEA visits, etc.), we have to use the car.
More selfishly, it also means fewer trips to the swimming pool or the bigger parks as there are no direct bus routes available and it's impractical to ask a three-year-old to cycle across several busy junctions and roads for two miles.
How did you cope? Taxis, car share lifts or just accepting that you can't do certain things? I would happily consider a rental club, but they don't appear to exist where I live. Public transport is nowhere near as good as London's.