I find it difficult to believe that humidity had any part to play in the performance of the aircraft (carb ice and airframe/induction icing notwithstanding).
The difference in density between dry and saturated air is negligible at the temperatures pertaining for this accident. A measurable difference first occurs at about 25C. At 50C the difference in density is about 5%. At 65C it is about 10%.
Indeed, the effect of humidity is almost insignificant compared to the effect of temperature and pressure. From the Heathrow METARs, one would expect a temperature of about 8 or 9 degC, and a QNH around 1020 hPa. That leads me to believe that the density altitude at Chalgrove, 240 ft amsl, was more than 500 ft
below sea level on the day.