240v Lights on a 12v Circuit?
If you look more closely at the link, the bulbs are actually for mains voltages, in one of the pictures, it states "Input Voltage 90V-264V". This is the voltage that needs to be provided to the bulb, and the voltage is then internally stepped down to 12V for the LED modules. So in this case, the name of the product is misleading. If you look at the fitting, this is the "E27" fitting, which is an industry standard, and so you should expect any bulb that will fit in this fitting will be for mains voltage.

Answering your question about the cable, the cable is designed for use at 240V, and will have a certain rated current. If you stay within these limits, the cables should be fine to use at lower currents or voltages. 

LEDs are normally powered by DC voltages. Either they accept a lower DC voltage, or have a built in circuit to rectify and reduce the input voltage. If you decide to buy LED lights that accept 12V input, a transformer alone will only give AC voltage. It is possible to find 12V DC plug in transformers which could work for powering LEDs, but you will need to check that it can provide enough current.

Also it is possible that you might encounter problems with the length of the cable. This will depend on the cable length, the cable core diameter, and amount of current you need to provide to the lights, but resistive losses could result in a loss of a few volts, which could mean the lights don't work, or at least won't illuminate fully.