Neo-liberalism is a direct challenge to democracy and socialism. It seeks to offer an alternative to political democracy as we understand it substituting it with consumers through the market. As far as possible, they argue, state provision needs to be replaced by private provision accountable only through purchase and contractual relationships. It is a hollowing out of democracy as we know it and as such is a direct challenge to the democratic state route that Labour has largely supported. Privatisation is also a direct challenge to socialism through restrictions on state aid in the EU and the World Trade Organisation (WTO) and in particular the General Agreement on Tariffs and Services (GATS) which lock provision into the market once it is de-nationalised: you cannot go back. So it seems any challenge to private ownership and the market which is implied by democratic socialism is a structural challenge to how capitalism now works as a whole.
What do we do about this as a Party?
Here are some sources which refer to alternatives:
This is just the tip of the iceberg - please add more.