I'm not sure where you're getting the numbers that 2/3s of people want Brexit to happen, as I can't find any that do.

Here's some more realistic numbers-

> The survey by polling firm YouGov showed that if a referendum were held immediately, 46 percent would vote to remain, 39 percent would vote to leave, and the rest either did not know, would not vote, or refused to answer the question.

https://www.cnbc.com/2019/01/06/britons-would-now-vote-to-st...

Here's an aggregate of polls that show much stronger support for "stay" than "leave":

https://whatukthinks.org/eu/questions/if-a-second-eu-referen...