Nonsense, you don't need to get into a top university to get into ship broking. I managed it with a Physiology degree from Glasgow. You are more likely to get into a graduate scheme, but they are only with Maersk, ICAP and Clarksons. I didn't include my degree on my CV apart from those graduate schemes (despite being a 2.1), as it wasn't relevant, and most ship-brokers don't think its relevant. Hell, most brokers don't have a degree.
Yes it's a closed door industry, but that just makes it more rewarding when you do get in. If you can sell yourself well with the little shipping experience you have, and can talk your way through a technical interview, then you are ahead of a lot of people coming fresh out of uni
So, simply put
Do the ICS foundation diploma, Increase your knowledge. More info can be found here,
http://www.ics.org.uk (Note, I would recommend doing Introduction to shipping and shipping business as your first modules, simply because you don't want to specialise before you've even got a trainee role)
Network with people in shipping (linkedin is a start, join some maritime industry groups), try get some work experience, whether its a couple of weeks or a couple of months.
Send your CV to everyone possible. Phone people up, physically walk into offices (This is what worked for me). It doesn't even need to be broking houses, send your CV's to shipping agents, freight forwarders, shipowners, ship insurance underwriters etc etc. Just get a list of names you can drop. Who you know is important in shipping, they will look for family ties to shipping, but just make sure you can demonstrate why you are better educated in the subject than the guy born into it.
Drop me a line if you have any more questions.