If you wish to add a light fixture it is best to extend the wire from the existing light fixture or connect the new fixture wiring at the switch box where the existing fixture is fed from. Running a spur from a ceiling rose.

Dynamo Led Light Systems For Bicycles Electronic Circuits
Adding a light to a circuit. Deciding on which method to use depends on your existing lighting circuits. Adding a light to a circuit an end of run fixture is one that goes after the existing fixture in the circuit. Probably the easiest way to wire up a new circuit is to break into the existing circuit and fit a new junction box. Choose a place for the fixture install an electrical box and run a cable between the new fixture and the existing one. With the light switch turned off hold the noncontact voltage detector against each of the wires connected to the switch. The supply cable to the new lighting point can then be run from there.
This is the hot wire and the one youll connect to the hot side of the new double switch. Take note of which wire causes the tester to light up. Adding a light to a circuit turn off all power supply to the room in which you will be working. Prepare the cable route for the spur from the last ceiling rose on the loop in circuit to the new lighting point. Touch the remaining prong from the tester to any metal on the electrical box or switch. Check that there is no power running through the wires with a circuit tester.
Touch a prong from a two prong electrical tester to a terminal screw holding a black wire to the switch. Cut off the power supply to the relevant circuit from the consumer unit. Make sure the cable you use is the same gauge as the one powering the existing fixture. New cable is run from the receptacle to the new fixture location and a switch loop cable is run from there to the new switch location. Enjoy your new light fixture. Prepare the cable route for the switch cable from the rose to the new.
Drill a pilot hole through the ceiling where you would like to install your ceiling electrical box. This drawing shows the wiring for adding a new light and switch with the fixture coming first in the circuit. The switch loop is a 3 wire cable to comply with nec requirements of a neutral in all new switch boxes. Remove the screws holding the wall plate to the switch on the circuit. This way you will be sure not to interfere with the wiring that is dedicated for the 3 way switches at each end of the stairs. The tester wont light if the correct breaker is turned off.