Costs of having a car?

Hope this is correct place.

My father told me that I need to buy a car for the uni. I refused, citing the cost and my general dislike for car (Sorry r/cars/).

At moment, I use public transport to get to college and this takes 1 hour each way.

However at the uni. It will take around 1.5 to 2 hours on public transport each way.

After refusing the offer. I've realised that this might be valid alternative.

Currently I live in the UK and distance to uni from my house is about 15-20 miles.

I have stable income at around £75 per week and parents are willing to add £25 on that. I live in extremely rough area, I think insurance will be as high as possible. Also, I'm aged under 20.

I can afford up to £5k for car. So, is this possible?

EDIT: Insurance quotes are very expensive, lowest being 17.5k and highest being 48.5k for Vauxhall corsa. I give up.

Thanks for trying to help, I shall upvote you all.