Ed Miliband gave Jeremy Corbyn greater backing than some shadow cabinet members when he appeared on the Today programme this morning. Asked whether his successor was suited to being prime minister, he replied: "Of course. In the end that’s a decision for the electorate, as I discovered to my cost. That’s a decision the electorate has to make." By contrast, when asked whether Corbyn and John McDonnell were suitable to hold "the highest offices in the land", Angela Eagle said: "I work with people the party gives me to work with".

Miliband went on to promise not to be a "back-seat driver" (prompting presenter Jim Naughtie to reply: "Well, having crashed the car it's difficult to do that") and said of Corbyn's programme: “He’s going to argue it in his own way and he’s set out what he believes is his mandate for, which is anti-austerity, a different approach to foreign policy and participatory politics".

But while the Labour leader's project is certainly distinct from that of his predecessor there is significant, and often overlooked, continuity between them. In its radicalisation of pre-existing stances, Corbyn's approach could be defined as "Miliband max".

It was under Miliband that Labour first identified as an "anti-austerity" party, with the then leader addressing the 2011 anti-cuts march. Though this stance was later abandoned, as emphasis was put on the need for public spending reductions (though with room left to borrow for investment), it helped create the political space which Corbyn later exploited.

It was also Miliband who denounced the Iraq war and promised a new approach to foreign policy, declaring in his 2010 conference speech: "Our alliance with America is incredibly important to us but we must always remember that our values must shape the alliances that we form and any military action that we take." His refusal to support the government's proposed intervention in Syria in 2013 was hailed by him as preventing a "rush to war". By promising "a different kind of foreign policy - based on a new and more independent relationship with the rest of the world", and opposing all recent military actions, Corbyn has travelled further down a road taken by Miliband. The Labour leader's promise to give greater power to party members ("participatory politics") similarly follows Miliband's decision to give them the ultimate say over the leadership (the system that enabled Corbyn's victory). Rail renationalisation, limits on media ownership and opposition to privatisation were also stances either fully or partly embraced between 2010 and 2015.

Many of those who voted for Corbyn voted for Miliband in 2010 or joined after being attracted by his radical moments. For them, Corbyn, the only candidate to position himself to Miliband's left from the start of the contest, was the natural choice. It was these left-leaning members, not Trotskyist entryists, who enabled the Labour leader's landslide victory.

The continuity extends to personnel as well as policy. Simon Fletcher, Corbyn's chief of staff, was Miliband's trade union liaison officer, while Jon Trickett, the shadow communities secretary (and a Corbyn supporter), was a senior adviser. If Miliband appears more open to the Labour leader's project than others, it may be because he recognises how much it has in common with his own.