The New York Times had a piece explaining what austerity (i.e. cuts in social services) has meant for the United Kingdom. While it is a useful account, at one point the piece tells readers:
"The austerity measures were imposed to eliminate budget deficits that ballooned to unsustainable levels in the aftermath of the financial crisis."
This seems to imply that the cuts were somehow economically necessary. This is not true. At the time, the UK had high rates of unemployment and large amounts of underutilized resources. There was no reason that it could not have continued to run deficits that were high because the economy was weak.
If the government had continued to run large deficits as the economy strengthened and approached full employment levels of output, it would have created inflationary pressures. This presumably would have resulted in the Bank of England pushing up interest rates to slow the economy, with negative hits to investment, housing, and the trade deficit.
However, at the time the budget cuts were put in place, there was no reason for the government to reduce its deficit. To say that it could not run deficits of that size forever is true in the same way that someone driving west in New Jersey can't keep going that way because they will eventually fall into the Pacific ocean. But that is not the reason most people in New Jersey stop driving west.