House hunting in London is a rather particular experience which it can take some time to really understand. I recently wrote a quite detailed post about this on my personal blog here, but as I was writing I realised that there are some specific considerations for anyone in consulting.
When I joined Accenture I was moving to London for the first time, but I did know some people already here. I was lucky enough to be able to stay with friends for the first couple of weeks' training in London, and decided to look for something more permanent after the Chicago training by which time I would hopefully know where my first project would be based. If you don't have friends to crash with there are plenty of short term lets available.
I would definitely recommend postponing any sort of commitment to a flat until you know where that first project will be. Many analyst roles are out of town. If you will only be in London from Thursday evening to Monday morning of each week, you're going to resent paying high London rent so will probably want to look for something on the cheaper end of your budget. Some out of town roles even include a flat so you may not need to bother about anything in London. Even if you are based in the city it's worth understanding where your office will be so you can factor that commute into your decision on which area of London to move to.
This is not always possible though. I am currently house hunting because my landlady is selling up, and this has coincided with a period where I am between projects. Trying to figure out where to live when you don't know where you will be working is not ideal but sometimes can't be avoided. The main thing to consider is having multiple transport links, whether that's tube, rail or bus, or a combination. Personally, one of the best areas of London I have found for this is West Hampstead. It's on a main rail route which can take you straight to the city, St Pancras, Luton and Gatwick; it's also on the super fast Jubilee line as well as the Overground, and Bakerloo and Metropolitan lines are also within walking distance at Kilburn and Finchley Road. It is even near a bus route straight from Stansted airport - pretty much the only airport it's more difficult to get to is London City but even that's not too bad.
I'm sure there are plenty of other well connected areas I don't know about. Make sure to look at trains as well as just the tube. And a long commute isn't necessarily the end of the world - most people would rather have a longer journey with a seat than a shorter one standing up in a carriage so overcrowded that you don't even have space to open your newspaper!