There's an ongoing debate about the practice of facadism, which considers the value of leaving an historic facade in place while the building behind is torn away. As a result, the facade is arguably nothing more than decoration, shorn of its original significance: "a cute toy designed to make a skyscraper more palatable". If done clumsily, it can also look incongruous in its modern surroundings (for me, the Lloyds Building falls into that category).
On the other hand, at least part of a building survives where it might otherwise have disappeared forever. Done well, the contrast between old and new can have its own appeal (here's an interesting French example). And as Matt Edgar points out, some buildings were essentially false facades to begin with: grand frontages often hid simple buildings in cheaper materials.
However, even the fiercest defenders of the practice would surely gulp at the sight of this effort on the corner of Artillery Lane and Gun Street, Spitalfields. The former facade is left orphaned from the rest of the built environment, large metal pins carefully holding it at arm's length from the new building. Its windows are not only blank and empty, but out of kilter with those added behind. If those responsible had spray-painted 'we only left this because they made us' across one wall and 'we hate old buildings' on the other, the message would hardly be less subtle.
I really hope that this is London's worst example. If you do know of any other contenders, share them in the comments.