dc42:
The page you linked to indicates that those LEDs are designed to work from a constant 12v supply and take not more than 3A. Presumably, this means around 1A per colour. So to dim them, all you need to do is to switch 12V to them using PWM. Start with a regulated high-current 12V supply, perhaps a standard ATX supply. If you want to use TLC5940s, then I would use P-channel mosfets to do the switching. They don't need to be logic level ones, something like IRF9530 will do. Connect source to +12V, drain to the +ve side of the LED strip, and gate to TLC output. Also connect a pullup resistor of around 1K ohms between the gate and +12v. Connect the negative side of the LED strip to ground. [EDIT: set the TLC current to around 20mA, i.e. more than the 12mA that will be sourced through the 1K resistors, to ensure that the TLC outputs saturate.]A slightly cheaper option would be to use PNP darlington transistors in place of the mosfets, with base series resistors instead of the pullup resistors. However, you would then need to increase the supply voltage to around 14V to get full brightness.
This is working nicely, but I have just realized the LED strips I have are common anode 
Could I use the IRF9530's to run them somehow?