Is it a fact that austerity killed 120,000 people? No. It comes from a modelling study which assumes the slowdown in life expectancy between 2012 and 2014 was caused by the govt, even though the same thing happened in other countries.
The authors then used their model to project what would happen in 2016 and 2017. It was a highly speculative and politically motivated article. https://bmjopen.bmj.com/content/7/11/e017722
Full Fact covered it here. https://fullfact.org/health/austerity-120000-unnecessary-deaths/
More or Less also looked at this factoid recently. Worth a listen. https://www.bbc.co.uk/sounds/play/m0008r63
Channel 4's fact checking site also covered the claim and came to a similar conclusion. https://www.channel4.com/news/factcheck/factcheck-did-austerity-kill-120000-people