BT had Cellnet, which became O2.
Three’s owner, Hutchison, owned half of Orange. They sold Orange to France Telecom.
Mercury (later Cable & Wireless) owned One 2 One, which became T-Mobile.
Obviously the last two merged to form Everything Everywhere, which was such a ridiculous name it got shortened to EE. BT bought the combined company from France Telecom and Deutsche Telekom.
My first mobile phone was an Ericsson T10 on One2One back in 1999 lol. Amazing how far things have come.