Anyone who talks about New Labour as being a “disciple of neoliberalism” really should define what they mean by neoliberal. One of the defining characteristics of neoliberalism as far as I am concerned is a dislike of ‘big government’. Neoliberals are not libertarians: they are happy to use the state and make it powerful in particular ways (e.g. defence). However neoliberals are in favour of the privatisation of many government activities, and cutting its welfare and redistributive roles. That is the only reason why austerity was a neoliberal policy.
There are lots of ways of measuring the size of the UK government, but here is one: government consumption as a share of GDP, using world bank data.
The share of UK government spending on this measure, as with others, rose steadily and significantly under the 1997-2010 Labour government. The contrast with the previous Conservative government could not be clearer. The positive benefit that brought to public services like the NHS was real and substantial.
There are other ways in which New Labour attempted to undo the impact of the market. One concerned child poverty. While they did not manage to reverse the increase in child poverty that occurred under Thatcher, it was not for want of trying. Relaxed about the inequality that came with neoliberalism for sure, but not relaxed about poverty. New Labour introduced the minimum wage.
New Labour could be described as neoliberal in some of the other things it did, or did not do. But true disciples do not usually pick and choose which of their leader’s teachings they follow. When it comes to the rather important issue of the size of the state, New Labour was not neoliberal.