The start-up, to be called My Agency, had been set to launch in June.
However, its launch was delayed after Law approached them about becoming the London arm of his network.
Talks ended when White and Wright decided to focus on the UK market rather than be part of a global network.
Based in Clerkenwell, My Agency has a core management team of four people.
Robin Lauffer, a former head of strategic and consumer insight at Euro RSCG and previously the head of strategy at McCann, joins White, Wright and Matt Turner, the former head of McCann Financial, in the venture.
The four will team up with other agencies and freelances to provide an integrated offering. Clients will be allowed to create their own agency from the talent pool, based on their requirements. Its first retained client is the computer processing company AMD.
Wright said: "Too many clients are saying that there is a lack of shared ownership and partnership with their agencies. My Agency seeks to redress the balance."