London is actually surprisingly cheaper than many cities in US. You just have to find your place based on the budget. I lived in Ealing area (sure it’s far from many actions but lots of great ethnic food in far cheaper price than anywhere else) in a quite a spacious apartment and it was half as much as what I spent in both two cities I have lived in US. And the tube is excellent (compared to our public transport standard). I actually somewhat miss my time there. It was safe (again based on my standard in US) and I didn’t really need a car.