All the above are correct, and Antoni knows his stuff (haven't seen/heard him around online for a while).
Here is a little more background.
The black and white undersides were, as stated above, an IFF marking. They arose as part of the coordinated air defence system the British were developing in the 1930s. One of the major problems facing the system, before electronic IFF, was to find a means of identifying friendly aircraft from the ground. This would allow them to avoid being shot at or shot down by friendly anti aircraft units and allow them to be tracked by the Observer Corps (not yet Royal). The early Chain Home radar system illuminated 360 degrees, but to allow operators to determine from which direction signals were returned the inland 180 degrees was blocked out electronically. This meant there was no coverage inland and all the plotting information which was required for a successful interception, such as the location of the fighters relative to the raiders after they had crossed the coast, had to be obtained visually by the Observer Corps. Dowding first wrote to the Air Ministry as early as 10th May 1937 suggesting that the underside of one of the lower mainplanes (of the mainly biplanes then in service) should be finished in the standard silver dope, and the other in black. On 28th July the Air Ministry gave permission for an experiment with the marking to be carried out. The experimental flights were carried out at North Weald, and on 28th October Dowding wrote to the Air Ministry informing them of the success of the experiments and, at the same time, suggesting that with Hawker Hurricane production gathering pace, the undersides of the wings of these aircraft should be finished black on the port side, white on the starboard side. Furthermore serial numbers, usually applied to the undersides of the wings at the time, should be omitted to make the markings more obvious. It was at this time that the large scale service trial on the 50 Hurricanes mentioned above was approved.
Cheers
Steve