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Currently I have a Daihatsu Charade 2005 that is fitted with 155/65R13 tyre's. These are what was fitted to the vehicle since new. I've been shopping around for two new front Tyre's and one Tyre shop suggested that I can get a better price if I fitted 155/80R13 Tyre's. From a technical point of view how does this affect the vehicles road handling. I understand that this how increase the wheel size and affect the speedometer calibration but I'd like to understand the effects on road holding stability on both dry and wet roads.

This would not be recommended. As you say, speed calibration would be compromised (you'll be going faster than the speedo reads), plus the height of the tyre wall will mean the tyres will flex and roll more on the rims when cornering. Also, the tyres may rub on the inner guard and potentially bind when the steering is on full lock.
Definitely not worth doing for the sake of a few dollars, especially when 155/65/R13s are not all that expensive anyway.

Thanks your reply is in line with both the vehicle manufactures and more honest tyre shops response when asked the same question. Further research show that if total diameter changes more than 5% a low volume certification is required according to NZTA.