Do you live in central London? I think it's a fairly unusual situation (in the country as a whole) to imagine that you'll never once need to travel with your baby in a car for their first three years or so until they can safely use a more portable booster seat. Maybe in the middle of a city it's less strange, but for most of us who don't live in that situation, you end up using cars sometimes even if it's a taxi, relative/friend's car etc.
Also I would think that most people do get some kind of car ride back home from hospital - whether again that's a taxi or a friend gives them a lift. Obviously not everyone drives or lives with a driver, but most people know somebody with a car, and it would be a very heartless friend/relative who expected a new mum to get the bus, or walk (more than 10 mins) home from hospital while still recovering from childbirth!
You can get a legally approved car seat that goes from birth-18kg (about 3-4 years) for about £40, or an infant carrier for £35 if you're really strapped. I don't like the £40 combination seat, and I would recommend you spend a bit more if you can afford to, but it will have passed a basic crash test in order to be sold and is much safer than using nothing at all (even though this is perfectly legal in a taxi). The £35 infant carrier is fine and will last 1-2 years depending on the size of the baby.
It's also perfectly legal to buy and use second hand car seats - just be aware that there are risks involved in doing that. I'd probably do it if I was going to travel in a car very infrequently, I wouldn't buy a second hand one to keep as my main car seat in my own car.