The Blairites learned the lesson of the disastrous SDP. What they did instead was hijack an existing party at a low ebb, they told the Labour Party that the problem facing the Party was the Party itself and they set about grafting a new party, New Labour, on top of the old one and assumed the graft would take, gradually taking over the whole party, it never did, but it did take over the PLP with Blair place men and Blair babes. But the whole New Labour project was so facile, so lacking in the essentials that make the Labour Party the Labour Party, such as a commitment to social justice, that the whole candy floss confection fell in on itself. But despite the setback of not getting David Miliband elected leader, the Blairites assumed that after a flirtation with soft left Ed the membership would fall behind a Blair clone. It is a testimony to their alienation from the membership that the tsunami that washed them away, twice, came as such a surprise.
Corbyn says he's an inclusive man and he is and the wayward Blairite sons and daughters will be welcomed back, but not straight away, a good number of people came on board when the party needed them most, he's not going to jettison them. Nevertheless, Corbyn needs the right wing of the Labour party, they've always existed in this broad church, but the left is in ascendancy, to use the old phrase Corbyn has to tell the Blairites "we're the masters now".