I was once going to buy a car to do up, which had brakes, but the aforementioned brakes were located in the boot. This lead to much brainstorming about how to transfer the car from it's current location to where I wanted it without resorting to having it towed.

I didn't end up buying the car.

Obviously, this makes me the expert on driving cars without brakes. The most important thing to do, after you've pumped the brake pedal and still found it unresponsive is not to shift into neutral, but to change to the lowest gear possible, either first or second in a manual. Most automatics have low gears too for use in steep ascents or towing heavy loads (in the cars I'm familiar with they're labelled '2' or '3'). You've probably never used them before, but now is the time. If you've ever tried shifting into second while travelling at speed, you will know that there is an explosive decelleration and the engine will scream. More importantly, there will be very little loss of traction as all the wheels are still moving - This is a safe way of washing off speed in wet or icy conditions, and the instruction manual for my car actually recommends this on steep descents to control your speed. If you have a lot of time, you can downshift in stages to save the strain on your engine.

By the time you've changed into a low gear, you should be travelling slow enough to gently apply the handbrake. Don't jam it on, as most likely you'll still be travelling fast enough to skid.
mkb and rougevert pointed out quite rightly that often the low gears on a manual are labelled 'L' and 'S' instead of '2' and '3', which makes 'DSL' if you're a nerd, and 'LSD' if you're a druggie.