How to find a recruiter with relationships at a specific IB (RBS)

Hi, I'm targeting a certain IB, RBS in Stamford. I have great experience, what I don't have are any contacts there. I think the best bet is to find a recruiter with a good relationships at RBS, but I'm wondering how to find a well connected recruiter. Any recruiter I ask will say 'oh sure I know everyone at RBS' whether they do or not. I could call RBS and ask who they like to work with, is that reasonable? They would probably say I should apply directly via their website, in which case my resume will go into endless limbo (if they operate anything like everywhere else I've worked) Anyone have a solution? I was thinking about doing a search on linkedin. Thx