I was forced to give up my car when splitting with my ex (shared car, he kept it) and I was far too skint in the first 6 months to contemplate replacing it - I was gutted about not having it any more, didn't know how I'd manage without it long-term and thought I'd replace it as soon as I'd got back on my feet.
A few years down the line, I'm still using the local buses and the occasional taxi (honestly, it's cheaper to occasionally take a £30-£40 taxi journey than to run and maintain a car all year round), and trains to visit family who live a few hours away (tickets aren't cheap, but neither is petrol). I've switched to getting my groceries and other big purchases online (works well for us as DH works from home, so there's always someone in to take in deliveries).
I'm starting to see car ownership as a luxury rather than a necessity, for us in our current circumstances at least. I do quite miss being able to do stuff on a whim (visit local attractions, friends in next town, that sort of thing) - travelling now involves much more forward planning and usually takes about 50%-100% longer to get anywhere. We'll have a family soon(ish) and I feel this will change everything. Until then, it takes much lower priority than the other costly stuff we have queued up (deposit for our house, holiday, OU course, and getting our finances in order ready to start a family).
My biggest fear about being car-less was having an emergency at home and needing to get somewhere in a hurry, but we faced this a few weeks ago when DH fell through a plate glass window and needed to go to A&E, we took a taxi (wasn't quite bad enough to justify an ambulance), and we had absolutely no problems - it was prompt (prob due to us giving A&E as the destination!), driver was friendly and really helpful, and we didn't have to worry about getting lost or parking etc. I no longer worry about emergencies like this, I know we'll be fine.
If you're uncertain how it will affect you, can you take your current car off the road when the tax expires, and just see how things go? Maybe put your usual car monies (tax, insurance, petrol, MOT, parking expenses, etc) in a savings account, deduct your bus/train/taxi expenses from it, and see where it leaves you? If you decide it's not working for you it won't take very long to put your car back on the road.