So if the aim is to save money (and assuming you’re not in-state for a public target school), go somewhere cheap/free for undergrad, do well, and get in to a target school’s master’s program. Or land one of those few big scholarships offered by the handful of target schools that offer them (basically Duke; maybe some others).
Even from an elite uni in the UK, breaking in to IB in the US would be tough as, well, you wouldn’t be in the US. That makes getting involved in any US recruiting difficult.
For London, the top feeders in to the City are Oxbridge, LSE, Warwick, and UCL. Obviously being British or European would help there, though.