My bike brakes are lethal, help! I've got an old Raleigh Winner (1980s 10 speed racer) which is perfect in almost every single way for what I need it for (I got given it free, it's very speedy and also looks cool).

However, the brakes are dodgy to say the least. I had to take the rear brake off entirely the other week as the bit that holds the cable in the brake lever fell off (mildly alarming as I was trying to stop at the time!). I haven't replaced it yet as it was basically useless before, should I bother?

In the dry, the front brake is incredibly squeaky but very effective (I adjusted the toe the other week?) In the wet though, it just won't stop and it's bloody frightening! I think the brakes might be cantilevers (they've got two wire spring things on pivoting arms) but they're so useless in the wet! Admittedly, I think the brake blocks are probably as old as the bike, but why are they so bad in the wet compared to the dry? Freewheeling to a stop is nearly as effective (and when/if the brakes do eventually bite, they whole bike vibrates and judders, it's very odd)! The tyres seem to be fine as well.

Would some new brake blocks and/or cables solve the problem (the rims are steel, which apparently makes a difference)? I'm a student so I'm hardly drowning in the dolla and also a bike n00b so I'm not great on the technicalities. What should I do?

Cheers.
There are a lot of things that could be wrong and a picture of the bike might help confirm this, so I'll just make a list of some things to check and what they need (this is by no means comprehensive):

1) Brake pads -- if they're old, they've likely dried out. Replace them. Needs a hex key. Make sure they're also hitting the rim and not rubbing anywhere. Also, clean the rims with rubbing alcohol (or if you're a student, vodka). 

2) Brake cables -- these can rust or the lining of the cables can be worn out making them not work properly. You need a housing cutter/dremel + awl + file to do this. 

3) Adjust the brakes. They look like single pivot sidepull brakes from google images, and you can find directions to adjust them here. You need probably a hex key and maybe a screwdriver. Also, make sure the caliper is secured to the frame. 

4) The judder could be lots of things -- theres a certain amount of judder on all bikes. Could be a loose headset (is the fork moving when you hold the front brake and try to move the bike?). Or it might go away if you fix 1-3. 

My suggestion is that if you don't know much about bikes or don't have someone to help you is to take the bike to a bike shop to get it checked out and see what needs repair, since you may not have all the tools you need to fix it or the expertise. You need both brakes in case one fails.