When going from old tires to new tires of the same size, does this affect the speed of your car? And if so by how much? Especially considering photo radar all over the city!!
If going from worn out to brand new tires of the same size, the difference in speed which is shown on the speedometer will be negligible. There may be a 1-2% difference, but understand manufacturers normally calibrate their speedometers to show faster than the vehicle is actually traveling. This is especially true in European countries (I understand there's actually a law which requires vehicles to over report the speed - I don't know the validity of this, but is what has been reported in other answers here on Mechanics.SE).
Overall, the vehicle will be closer to showing the correct speed with new tires, but should not be showing slower than the actual speed the vehicle is traveling (as long as everything else is accounted for and is mechanically correct).
Hmmm, most tire calculators take tire dimensions, but you can easily calculate it yourself.
My car has cute 155/70 R13 tires. 155mm is the width, and 155mm*70%=108.5mm is the height of the side wall. Rim diameter is 13"=330,2mm, and one has to add two times the side wall height to get the total diameter of 547.2mm. This multiplied by pi gives the circumference.
New tires come with tread depths of 8-9mm, and old ones should be replaced before there's no tread left. Here in Europe, the minimum is 1.6mm (summer tires). So tires loose up to 2x7.4mm=14.8mm in diameter, and mine end up with 532.4mm. Now, the ratio of circumference is
547.2mm * pi ------------ = 1.028 532.4mm * pi
I.e. the new tire has 2.8% more circumference than the worn, and the car is 2.8% faster at same indicated speed (same RPM).
As said, my tires are tiny (but great in snow), the effect becomes smaller with larger tires.
Concerning speed cameras, Paulster is right, at least here, the indicated speed must never be lower than the real speed. If someone decides to mount very large wheels, the tachometer has to be adjusted.
I'm not a judge (nor is this the right place), but if you were speeding, discussing tire sizes shouldn't help. I guess if your car displays a too low speed due to too large tires, it's your problem almost everywhere on earth.