The government does have plans to cut some taxes but most of the money is simply going nowhere, in the current conditions austerity is destructive. Because it keeps the economy operating under its potential, it makes everyone poorer. It's not always true but at the moment the government could very easily borrow more, spend more, make everyone richer and yet have a sustainable budget.
The key insight in all this is that a government is not like a household. If you reduces spending (say stop going to the restaurant), this has no effect on the economy so you are still earning the same income and you will have more money available, e.g. to pay your debts. So as long as everyone else is still spending and your job is not at risk, cutting on expenses is a good way to increase your savings.
But if the government reduces spending, it will have a big effect on its revenue as well so, depending on the conditions (specifically whether the economy is operating at its full potential or suffering from a shortfall of demand and whether the central bank can compensate the effect of budget policy through monetary policy, neither of which have been true recently in the UK), it's entirely possible that it would gain very little.
That's why beyond all considerations regarding fairness, unemployment, poverty, etc. recent austerity programmes in Europe even fail at what is ostensibly their main objective, namely reducing the weight of the debt (relative to the GDP). The only thing austerity achieves (and perhaps that's the objective) is to permanently reduce the size of the state. That's true both in the euro area (which has specific structural problems) and in countries like the UK or Sweden (which don't face the same constraints but have adopted austerity policies nonetheless).
See also this essay by Paul Krugman and this short note by Simon Wren-Lewis (both have been writing a lot on all this over the years).