When Americans talk about the U.K., or for that matter about the U.S., there is generally no lazier, tireder, more meretricious cliche than the Churchill Invocation, in which it's always 1938 and always about Munich. Of course, whereas Churchill was bravely and farsightedly urging a benighted, unready country to stand tall against a brutal, ravening bully, in the U.S. it's generally invoked to support beating up on smaller, weaker, countries or for that matter civilian groups that, even if not as friendly as we might wish, are also not irredeemably hostile (unless and until we make them so).
And of course U.K. people, compared to those in the U.S., are likelier to know Churchill's full political history, which had low points in addition to the world-historic high point that we always have in mind (even when it's wholly off-point) on this side of the Pond.
But in the U.K., where the winning pro-Brexit forces were too cynical to have any plan, and the government decided not to make any plans, and where there is currently neither a functioning government nor an organized opposition, it's time to think about Churchill 1938, albeit at a greater level of abstraction.
Although I'm non-UK and obviously don't know the politics, I am getting the sense that Brexit is likely to happen, even though it still requires a set of deliberate political acts by people who already well know (or will soon find out) both (a) that it is unwise, and (b) that the public didn't choose it knowingly (as opposed to voting symbolically so as to "send a message," or else under the influence of false information). Plus, for that matter, the wrong public voted - to match voice with consequences, young people and future generations should have counted for more here than they did in the actual balloting.
But the reasons it seems likely to happen are (a) politicians in both of the major parties who know better are playing it safe or thinking small or treating it as "politics as usual," and (b) those with a large enough voice to do something individually, such as the U.K.'s own U.S.-born version of Trump, might prefer to see terrible things happen (even if they couldn't dodge the blame) than have to admit what a sham they've been playing out in public.
So if "being like Churchill" means being brave, and taking the long view, and not worrying about whether it's to one's current political advantage, or about who else will go along, or about whether it's good for one's current image, and if "being like Churchill" has no necessary connection to the particulars of the canonical 1938 Munich showdown, then at last it's time for it now. But takers seem likely to be in short supply.