I lived without a car for years.
Even now, with wifey using one, I rarely use it for anything other than family trips with the kids, and will be car-free for 3 weeks as wifey is away :-)
I found it relatively easy to live car-free but it does involve some investment to start with.
– Good waterproofs – top, legs, head, gloves, shoes,
– Brompton – opens up public transport, car lifts etc,
– Trailer – for supermarket shops,
– hack bike – full length mudguards, dynamo lights etc.
For trips to the tip etc you can use a trailer or there will be a local odd-job man who offers an uplift service. It costs £300+ a month to run a typical family car, with depreciation etc, and that's an awful lot of taxi fares.
Good luck!