The pilot noticed that during the descent and instrument approach the windscreen had become fogged up by condensation on the internal and external surfaces. Cabin temperature had been maintained at about 30 degrees Celsius during the flight in an attempt to reduce this effect. The weather at Brisbane at the time was drizzle with visibility reduced to 5000 metres, cloud 5 octas of stratus at 600 feet, 5 octas of stratus at 1000 feet, and 6 octas of strato cumulus at 1500 feet. Relative humidity was 95 per cent. After landing on runway 19, the aircraft was slowed to a slower than normal taxiing speed, due to the reduced visibility, and was taxied off the runway via taxiway "Alpha 5". The aircraft was not fitted with a windscreen defogger blower, which necessitated wiping the inside of the windscreen clear with a cloth in an attempt to improve visibility. There was no means of clearing the external surface. The aircraft was starting a right turn to enter taxiway "Bravo 5" when the Surface Movement Controller requested the pilot to enter the apron behind a Boeing 727 which was under tow. The pilot was unable to sight the Boeing 727, and forward visibility was severely reduced at that time by the effect of the bright apron floodlighting, which the pilot was facing. The result was, that after entering "Bravo 5", the aircraft ran off the taxiway, crossed the grass verge, and came to rest in a 2 metre deep drainage channel.