London 1st year analyst: how much to budget on rent?

As a 1st year I would try to be below 1.3-1.5k per month all in (utilities & council tax)

You should for the internship, not needed as a FT. 

If you mary me for the UK green card equivalent, we can split rent in a 2 bedroom flat

Ideally you do flat share for first couple of years of your career otherwise you'll end up paying close to 50% of your base salary just on accom, which is not ideal esp if you want to start saving / like to go out heavy on the w/e. 

Would suggest you consider a flat share with friends / fellow analysts - loads of people do it. This will help you to cut costs down to 0.9-1.2k all-in and will also let you afford a much better flat with a lounge and good location. Otherwise, you are likely to get stuck either with a tiny studio in a central location or one bed apartment in a shitty area.