It is possible to commute with bike+bus but you can't really bike in winters. So you have to rely on bus only. LTC has delays more often than not, which can get really frustrating in the winters.
When I was going to Western, I lived downtown and my car was constantly getting broke into. This was in the era where downtown was transforming from sketchy to absolute hellscape. Anyways it got to the point where I had to take it to my parents place and just leave it there. It was doable, but it wasn't the funnest. LTC is fairly robust though, I mean given Londons size, it's not the worst transit system by far.
Not only can I, I've been living without a car in London for a few years now. As people have said elsewhere in this thread, grocery shopping is a pain, but it's definitely doable. I think it helps that I live somewhere more or less central in town and not in suburbia hell. Like the real estate guys say: Location, location, location. It may or may not be possible to give up your car in London depending on where you live.