No personal experience but have relatives in the field so can share a little. No I don't think it's necessary these days to have connections, but to make it into the top banking positions where you earn the megabucks you need to be very, very bright, top academic results from a very good university (Oxbridge ideally), highly numerate and articulate and also have a certain personality type, not necessarily your archtypeal banker arsehole but certainly driven, confident, persuasive, able to cope well with pressure and work at speed, and absolutely prepared to dedicate your whole life (evenings, weekends, holidays etc) to work for a significant period of time, particularly while you are a junior but really for as long as you want to be earning the ££££. The best route is in graduate entry so have a google around their process and requirements.
That being said, being an 'investment banker' and 'working for an investment bank' or in the banking field are very different games, there are all sorts of other jobs that banks employ which although not paid the huge salaries, also don't come with such huge pressures. People I know that were interested in the industry but didn't quite make it or weren't quite suited to the pure banker or trader roles have gone into fields like compliance, security, accounting, management consulting, normally with a first degree in a vaguely mathematical/business oriented subject and then further post-grad qualifications, sometimes via a grad scheme or on the job. Don't know about apprenticeships but I expect there are some especially at the high street banks and these can be a good way in.
The hatred is complicated, partially simple dislike of anyone seen to earn a huge salary from moving money around and there can be a perception (partially justified) that banks make money off the failures of others and/or are parasites on the capitalistic system without actually doing anything to create wealth themselves. It's also partially a class issue where bankers are seen as 'new money' and therefore flashy, vulgar etc. Thing is nearly every single profession has its haters (lawyers, teachers, accountants, police, doctors, nurses, management consultants, GP receptionists 
the list goes on), particularly those that so if your son is ambitious and wants to make good money, particularly in a corporate field he'll have to learn to live with his profession being slagged off on the internet every so often, that or people just never having heard of it...