There have been a number of complaints that Starmer is becoming a 'centrist'. There is a problem with using the term 'centrist' in the contemporary political context, in that the 'centre' has been moving rightwards for a long time, away from the centre of gravity of much of British public opinion (see Tariq Ali, 'The extreme centre: a warning' (2015).) An added problem with the terms 'centre' and 'centrist' is that the right has been changing, both here and overseas, from a 'neoliberal' to a 'populist/nationalist' position. An unacknowledged factor in this assessment of Starmer as a 'centrist' is an unconscious assumption that Starmer's 'sartorial preferences' (see my blogpost in May on the subject of politicians' apparel) for sober suits and ties indicate that he is moving the party to the Right, just as Corbyn's deliberate casualness indicated that he was moving the party in the opposite direction. It may well be the case that Starmer is using his 'respectable' appearance to distract attention from the fact that, in imporatnt respects, he is keeping the party to the Left.
There is precious little evidence for this other than the dismissal of Rebecca Long-Bailey (see my blogpost of last month on this subject). He has said very little about the future direction of either economic policy or foreign policy. However, it is possible to deduce from the economixcs of coronavirus (requiring significant long-term State intervention and possible redistribution) and the climate of opinion within the Labour Party (which displays absolutely no appetite for a return to austerity or 'neoliberalism') that one of Corbyn's and McDonnell's permanent legacies to the Labour Party is an identifiably democratic socialist/green economic policy. Whether our departure from the EU makes an interventionist economic policy easier to pursue depends on your view of the gap between the theory and practice of the EU's policies in this area. From a historical perspective, although Labour's economic policies in the 2017 and 2019 elections were a departure from those of the Blair/Brown/Miliband years, they would have seemed completely unexceptional to Attlee or Wilson, when significant public ownership, exchange controls and prices and incomes policies were features of the economic landscape.
As far as foreign policy is concerned, the Corbyn era was the most leftwing since the pacifist leadership of George Lansbury (significantly more leftwing than that of Michael Foot, who was never a pacifist, as shown by his stances on the Falklands War and on appeasement in the 1930s). Corbyn has vocally supported Third World movements of national liberation, so he cannot be labelled a pacifist. Corbyn's not unjustified suspicion of the security services (see Stephen Dorril and Robin Ramsay, 'Smear! Wilson and the secret state' (1991), which documents long-term MI5 surveillance of Wilson, Tony Benn, Judith Hart et al), his understandable refusal to engage in a suicidal nuclear war (although it is important to note that official Labour policy supported Trident throughout the Corbyn years), and his equally understandable opposition to bloody foreign 'interventions', earned him the undying hostility of the Labour Right. (The row about antisemitism was a potent factor, but on its own does not explain the hostility to Corbyn). For these reasons, Corbyn could never escape the accusation by the Conservative press that he was 'unpatriotic.'
It appears that Labour is now returning to the pro-Atlanticist and pro-NATO positions which it has held since Attlee and Bevin. However, those assumptions presuppose an American president who was prepared to observe diplomatic niceties and hypocrises. The absence of such a president (and the likelihood that any successor will also display 'isolationist' tendencies) makes such an assumption seem like wishful thinking, if not actually delusional. The world has changed since 2015: there cannot be a return to the status quo ante.
However, the historical point remains. Labour is returning to its pre-Blair centre of gravity: social democratic/socialist in political economy, but in the area of foreign, defence and security policy , is profoundly respectful of the State in every way. The problem for the Labour Party is that if the United Kingdom is to survive, the role of the State needs to be fundamentally re-thought. Its historical over-centralisation, a tendency which has been exacerbated from 1918 onwards, is an obstacle to the co-existence of the nations of the United Kingdom and to the flourishing of its regions.