Haha...don't take this badly, but yep you are being a weanie

You will be fine. Walking around london is great. You really see things that you wouldn't if you were driving and the excercise will help make sure you don't gain weight from all the fab chocolate the UK has to offer.
As for walking after dark, well it gets dark here around 4pm right now, so the chances are high that you will have to brave that sooner rather than later. It's not any different than any other city, just be aware of your surroundings, stay on well lit/travelled roads and you will be fine. I have never once been bothered at night or day walking in London. I used to stay out quite late after work, catch the tube home and walk the 1/2 mile from the station to my flat no problem. If I had been drinking I normally kept my house keys in a pocket as opposed to my handbag, but that was the only real pre-caution I ever took. Luckily never needed it.
Good luck! You will be fine and adjust in no time.