Why are nations engaging in austerity when bond yields are historically low? In the UK and EU austerity programmes are rife. However, bond yields are also historically low, and have even been negative! At a time when debt is cheaper than ever, and below the accepted long term rate of inflation, why do governments not take this "free" money to maintain their states? Or, is it the austerity itself that is driving the rates?


UK bond yields:
http://www.tradingeconomics.com/united-kingdom/government-bond-yield
EU bond yields:
http://www.tradingeconomics.com/euro-area/government-bond-yield
Debt being cheaper than ever doesn't mean that it is optimal to borrow. Unless you plan to invest the borrowed money into projects that yield higher returns with certainty (we would call this arbitrage), any debt implies a tradeoff between the welfare of current versus future generations.


Perhaps the borrowing before to higher rates was non-optimal under the current government's perspective. I.e. now we place a higher value onto future generations versus current generations
Perhaps now in the slump, the government doesn't see investment opportunities that yield a sufficiently high return.
Perhaps the current government has a different prior on how high returns to debt are. Different governments (or the same government over time) can have a different prior (guess) on how important/productive government spending onto infrastructure, education, health, military etc. is. This also includes a prior on how large the Keynesian multiplier is, and how effective demand stimuli are. Then, even presented with the same investment opportunities at a
lower interest rate, a current government might chose differently
than the previous government.


This was all without political economy consideration. There are arguments on optimal spending that take into account how your current budget will affect the budget of future (different) governments. Have a look at Persson and Svensson (1989) to get a feel for this kind of political economy reasoning. 

Note that the argument in the cited paper would go the wrong way (i.e., too much spending of a conservative government), but it shows you how optimal policies under a permanent ruler can differ from optimal policies in a democracy.