OK this is a common problem on the MGF (i believe it was resolved with the later MY2K MGFs). Here's the lowdown...
How it works
Behind the brake pedal there is a plunger switch, the brake pedal is like an inverted L with the pivot at the corner of the two legs. With me so far? OK, what happens is this, when you depress the brake pedal, the assembly pivots around the corner, this converts the forward motion of the pedal into a lifting motion above the brake light switch, releasing the plunger and activating the brake lights.
The reason it becomes over sensitive is to do with the switch itself, it has in internal 'ratchet' like mechanism with self adjusts based on the pedal position at rest. If you catch the pedal by accident and lift it, the plunger is depressed further and it resets itself to this new position.
OK, the cure to this is really easy, but because you need to access the brake light switch access is a problem. I have found that the best way to get in there is to lie with you back on the seat base and your head in the footwell looking up at the pedals!
OK, once you are 'in the position' find the brake light switch, it is the ony thing in here with wires going to it. Rotate the brake switch through 90 degrees and it should come loose, allowing you to slide it out of the mounting. Remove the wires if necessary to give you some more room to work on the switch. Now, grasp the plunger firmly and pull (hard). It'll make a loud CRACK and extend anywhere up to 10mm or so. When extended you should see a notch in the plastic shaft. Reattatch the wires if necessary.
IMPORTANT! Because the switch is self adjusting, you must
hold the brake pedal depressed whilst you re-insert the switch. This keeps the pedal off the switch and prevents it resetting itself incorrectly (you'd have to do this all again if this happens).
Holding the brake pedal depressed
with one hand, slide the adjusted brake pedal switch up into it's keyhole mount and rotate through 90 degrees to secure. Now release the pedal
The short leg of the 'L' will rest on top of the switch and set it back to the correct position (you might hear it clicking when this happens).
Below is a sketch and a photo of the mechanism to help you get a better idea of what is involved and how it all works together.