There are different routes into investment banking.
The graduate scheme is the common way. But you'll find many people in the industry that started there careers doing something else, e.g. former accountants, lawyers, doctors, engineers etc.
The key in getting into Investment Banking is good academic credentials and good work experience, whether that be at another bank or working for a food company.
Would advice your boyfriend to apply to banks. If he graduated recently he might be better going for the graduate scheme (speak to HR about that, just call them up). Otherwise he could try as a lateral hire. It also depends whether he did a business related degree or not. If one did a Arts degree and was a teacher and now wanted to do investment banking, they would have to 'prove' their interest and commitment by doing a MSc or MBA in business/finance and then applying for a job (at least then you'd come in at the associate level).
Just contact the banks and ask. He should definetely go for it if he wants to. He may have to wait till September for the graduate scheme, hiring is pretty much done for the year but he definetely go for it.