Top economics courses are very competitive. He needs to consider carefully what he really wants to study and where his strengths lie.
Cambridge, LSE, UCL and Warwick are very mathematical, or perhaps more accurately statistical, so can be difficult for those who don't really love manipulating numbers. They are also really oversubscribed, so advice DS got was to apply to all four and be happy with a single offer, or treat it as a two year process and reapply. (He got three rejections but an offer from LSE. One of his peers got four rejections but Cambridge, not LSE, on reapplication.)
However you don't have to be able to crunch numbers to get into banking so it is worth looking at other degrees, for example Finance, or PPE at LSE, or management courses at UCL. And Bath, which offers some good placement years. Better he studies something he enjoys.
LSE has a good careers office and a lot go into banking. Being in London makes it easier, as there are network breakfast type events, where an economist from a bank will give a talk. And if you don't get a summer internship there is plenty of scope to sign up with a City temp agency to get some exposure to the working culture. That said, a quick look through Linked-In shows that plenty get to the City through less traditional routes, for example via back office operations in places like Bournemouth or Halifax, or with unrelated degrees.
The reverse happened with DS. About a term in, and with lots of exposure to would-be bankers, he decided it was not for him.