Corbyn has been accused of being out of date, with a political stance which is no longer relevant. What isn't discussed is that neoliberalism, which is what Thatcher and Reagan espoused, is a rehash of 19th Century ideas.
Privatization, fiscal austerity, deregulation, free trade, and reductions in government spending in order to enhance the role of the private sector in the economy have all been seen before.
Thatcher's friend Pinochet was the first to implement it and her guru Milton Friedman's monetarism was part of it. Her hero was Adam Smith, although she may have misunderstood his economic theory - there are those who believe Reagan made that mistake in the US.
Blair was also a neoliberalist, so both parties were following similar economic strategies, with only small differences.
The effects are that the poor get poorer and the rich get richer, as we have seen.
The previous reaction in the end to this type of ideology was the rise of Trades Unions and the Labour Party to protect the workers. In recent years the Labour Party has been unwilling to take on this role, but Corbyn's rise demonstrates the people's desire for someone who will redress the balance.
It's not that the membership have moved to the left, it's that the PLP have moved to the right.