Hasn't really changed us. We use our car to run errands and go for days out - picnics, festivals, historical sites, other family friendly outings. Trains are not cheap, and not really toddler and baby friendly. Before I got so pregnant, I walked to work (almost 5 miles round trip) to work and took a bus two days/week. Buses are 80p per ride/person, not buggy friendly and take forever. Our car is a compact, economical diesel that doesn't use much fuel.
We went w/o a car for about a year, but tbh, it was a REAL PITA w/a young family.