This thread poses an interesting question by the opening poster. If anyone looks back at the history of the Labour movement in Britain they will see that the Labour Party was born out of the growing workplace power of the trade unions at the beginning of the nineteen hundreds. It was, however, a realisation by those unions that not all the aspirations of working people in regard to better health care, housing etc could be brought about by way of workplace influence.
Therefore the Trade Union Congress was brought into being and that body initiated the formation of the Labour Party as it's political arm. Following that the parliamentary labour party was formed to bring forward candidates to fight for Labour movement representation in the House of Commons.
The Labour party remained closely aligned to its trade union roots throughout the early years of the nineteen hundreds. Evidence to the foregoing can be witnessed in the fact that many of the members of Cabinet in the 1945 Clement Attlee Labour government were from trade union backgrounds.
However, the trade Unions gradually relinquished ever more autonomy to the Labour Party during the period beginning with the1960s so as to grant greater speed and flexibility to the parliamentary Labour party in forming its policies and other actions. That parliamentary Labour Party autonomy reached its zenith under the leadership of Tony Blair when all trade union representation was eliminated from the Labour party National Executive Committee (NEC).
Further to the above, the influence of the Labour Party Constituency parties was then also drastically reduced when all candidates for palimentery seats were selected by the NEC and then "parachuted" into the constituencies with the local parties having no say in that selection whatsoever.
Many would argue that the above gave Britain a Tony Blair centre-right government which acted under the label of the Labour movement, but in fact, had virtually severed all communication and representation to that body. Again, many would argue that such a government without ties to its roots and not even accepting a reasonable level of representation from its own district and constituency parties, eventually brought Britain the beginnings of zero-hours contracts, the Gig Economy, the British side of the banking crisis and the Iraq war.
However, the election of Jeremy Corbyn as leader of the Parliamentary Labour Party in 2015, has brought action that has once again given the Labour party district and constituency parties far greater representation within the NEC, and perhaps most importantly the Broader Labour movement by way of the trade unions is also now once again well represented on that body. So, whatever the criticisms of Jeremy Corbyn, his legacy to the Labour Party and the broader Labour movement in the country will be the above structure, and many at the grassroots of the movement are and will be forever grateful.
Therefore those seeking "what is old labour" may look no further than what it is now.