Interesting, I didn't know giffgaff was actually directly related to O2 besided using their network. Out of curiosity, I tried to find some information on Three and got a little surprise: "In January 2015, Li Ka-shing entered into talks with Telefónica to buy its British mobile division O2 for around $15.4 billion. In March 2015, Li Ka-shing confirmed it will be purchasing Telefónica's UK mobile division for £10.25bn subject to regulatory approval by competition regulator, Ofcom." So it seems Three is going to own both O2 and giffgaff by buying Telefónica?
Source: https://en.wikipedia.org/wiki/Hutchison_Whampoa#History