The square wave you are seeing may be due to 50Hz mains pickup. You're in England (or Ireland/Scotland/Wales), I assume?
You can try a couple of things. First, check the frequency of the square wave. If it's 50 or 60Hz, it's mains interference. If you're running the circuit from batteries, you don't need high resistance in your electrodes. Try reducing the resistance to about 10k, that should significantly reduce the mains pickup.
If the square wave signal is in the frequency range you're interested in (200Hz...20kHz), then add a resistor of about 47k between each lead and ground. This will act as a voltage divider, and might be an easier way to reduce the signal voltage.
You should be seeing signals of only a few millivolts - maybe 50mV maximum. If you're seeing voltages in the volt range (1V or higher), then you're an antenna, and you're picking up voltage from somewhere else! Also, you'll find that any televisions in your area will tend to induce voltages in you. Turn off the telly, or better yet, go into the back yard/garage and try there if that's possible.
The only other thing I can think of is if you're living under power lines. They will cause you all sorts of problems, at all sorts of frequencies.
As someone suggested, maybe if you post a schematic (circuit), it will help to pinpoint any unusual problems or potential danger points.
Given that you connect your probes to each temple and one in the middle, I'm surprised you didn't turn into Frankenstein! Did smoke come out of your ears?
Let us know how you got on, it sounds an interesting project!