The IMF has told us that building infrastructure can pay for itself. This is, of course, true. However, we do need to be rather careful about the implications of that fact. for while it's entirely possible for something to pay for itself that doesn't mean that everything will do so:
The study finds that increased public infrastructure investment raises output in the short term by boosting demand and in the long term by raising the economy’s productive capacity. In a sample of advanced economies, an increase of 1 percentage point of GDP in investment spending raises the level of output by about 0.4 percent in the same year and by 1.5 percent four years after the increase (see chart, upper panel). In addition, the boost to GDP a country gets from increasing public infrastructure investment offsets the rise in debt, so that the public debt-to-GDP ratio does not rise (see chart, lower panel). In other words, public infrastructure investment could pay for itself if done correctly.
The words to concentrate upon are those last three "if done correctly". For no, this does not mean that bunging £40 billion at a train set will pay for itself. Nor that damming the Severn Estuary will nor any other of the various plans people are floating. As Greg Mankiw says:
Certainly this outcome is theoretically possible (just like self-financing tax cuts), but you can count me as skeptical about how often it will occur in practice (just like self-financing tax cuts). The human tendency for wishful thinking and the desire to avoid hard tradeoffs are so common that it is dangerous for a prominent institution like the IMF to encourage free-lunch thinking.
It still depends upon what you're building and where you're building it and how you're building it.