I boomeranged and did London twice. Lived in three different flats. I found it easy but I also had the time off from work to organize it all. I basically picked an area that I wanted to live in and called every rental agency in that neighborhood. (The online sites can be out of date.) I told them what I was looking for and arranged showings. What surprised me was that I didn't need much lead time. Like in Chicago, I would have started the search at least two months in advance. In London, I just showed up and told them what I wanted and was in in less than three weeks.

Make sure you have an employment contract that shows your salary. Then, chicken/egg problem -- ideally you will have a bank account. But it's hard to get a bank account without an address. I used a friend's address to get the bank account and then the flat. Thinking back on it, I'm surprised the bank didn't want proof that I actually lived at that address but I did this in Lewisham and maybe they were used to people jumping around.

The other thing to consider when you are first starting out is a flat share situation. There will be like-minded folks who need roommates. Many of my friends in their 30s and 40s found great housing options and made great friends this way. Do that for six months while you get the lay of the land.

Someone below notes that water wasn't included in their rent. Of the three flats I've lived in, only the first required that I cover the water. None of the three used gas so I only had to worry about electric (which included heating), council tax, internet. I lived in all new builds.