It shouldn't really cause the car to slow down. It uses more power, so you should see a slight increase in REVs, but no real loss of power.
If you have a facelift model with the digital AC rather than the three dials, then it is Climate Control, which can use more power some times. The climate control will use more power at first as it attempts to reach the pre-set temperature, and then less as it only needs to maintain the temperature.
Have you checked the Battery? It could be a problem with power supply as previously mentioned. I would ask your Mechanic to do a battery check, but then again, Kwik Fit or similar usually do a free Winter Check this time of year that includes a battery test.
Just noticed your audio in your signature. While it isn't too big, it will be using more power than the standard stereo. Do your lights dim slightly when the system is on loud?? You may find you need a power-cap. As the audio system is also using more power and then you throw the AC into the mix, you could be asking for too much power.
Maybe you could disconnect the Amp from the battery for a little while and see if things get better. Would be a quick way to find out if you need a power cap or not.