Hi there

Congratulations on your upcoming move. Without meaning to sound unpleasant, it is very, very difficult to answer your question without some lore information as there are literally hundreds of areas in London to live.

Some basic questions you would probably have to have answers for are:

Where will your work be based and how long of a commute do you want?
Do you mind taking the bus, walking or taking or changing trains?
What sort of an area do you want? Quiet, peaceful and middle class? Edgy, youthful and tragically hip?
Do you need to be near any airport?
What sort of budget are you operating under?

As a very broad rule of thumb (to which there are many exceptions, many of which our more pedantic members will no doubt take much pleasure in pointing out), you can look to spend around £1,500 per month for a two-bed flat in a decent area - although this can vary widely depending on time of year, demand and many other things.

Also note that rental property prices are quoted both weekly and monthly (often abbreviated to pcm, for "per calendar month"), sometimes have utilities included and sometimes don't, and sometimes are offered furnished bt usually aren't.

I await your reply.

Best wishes to you.