Go for it - think of all the money you will save and how you can use this for other forms of transport. Think too of the reduction in hassle.
When we lived in London, zone 2/3, we did it. We were not commuting to work by car and so used to only cover around 3,000 miles a year. We worked out that our 'fixed' costs were around £1500 a year (tax, insurance, MOT, servicing). Petrol was another £300-500 a year.
We used the £2000 or so saved to get the train, taxis and hire cars when needed. Biggest cost was hiring a car for holidays or weekends away but for 2 weeks a year or so this was still less than the cost of owning the car and we used to get taxis back from the supermarket etc if we had too much to take home walking or by bike.
We initially joined a car club which was very convenient but we found the subscription costs were quite high for the number of times we used it. We were lucky as we had several car hire places near us and so could usually get a car for the weekend for a cheaper rate. It was great to be able to drive a range of cars and get what was usually a brand new hire car which excited the children!
Now we are no longer in London unfortunately we have had to buy a car - there is not the network of public transport available and whilst we still walk and cycle a lot there is not car hire available to the same extent. We also have it in case of having to suddenly visit older parents in emergencies. plus my daughter seems to have started suffering from car sickness and cleaning up hire cars is not very pleasant!