You can’t miss the postmodern hulk known as No. 1 Poultry on a visit to London’s financial district, even if you wanted to.

A fevered concoction in candy-striped sandstone, the James Stirling-designed office complex occupies one of the most contested and debated sites in central London. It’s now due for resurrection in a new guise as an 11,000-square-foot facility leased and run by WeWork.

That a co-working company is guzzling big city office space isn’t in itself shocking; the building isn’t even…