Corbyn is in an english left group that basically are left british nationalists, this includes most of the trade union leaders he is close to including len mcluskey, it includes his closest political advisers and colleagus people like seamus milne (who I was friends with before), andrew murray and other. for many decades they have campaigned against the EU, played up a 'socialist' version of british nationalism that says that 'migration needs to be controlled', 'british jobs for british workers' etc.
Keep in kind that I was a national student advisor for Arthur Scargill, who, while out of politics in any meaningful way for decades, is nonetheless the greatest left-wing english socialist (nationalist) left, and I campaigned on his party's policies in the early 2000s which was clearly british nationalist, FOR immigration controls, and was basically competing for the far right back then, the northern racists were of course voting for the fascist BNP and increasingly ukip back then, that has come to full fruition with Corbyn competing with the far right for these votes. Of course in such a competition the far right ALWAYS wins.
Now Corbyn was a degree or two outside of this as he was an activist MP who wanted to make everyone, the left nationalists, the liberal nationalists and migrant communities happy. Including supporting head choppers (death squads like Moazzam Begg) and those getting getting head-chopped (Kurds) at the same time!
As Corbyn came into the leadership of the Labour Party, he has decided to go along with this left brit nationalist group.
Only the far left loyalists of Corbyn think he did a good job in the referendum on brexit, everyone else knows that he was 'hedging his bets', its an open secret that him and his group wanted to send a message to their core group - northern racist white working class older men - that they are not really against brexit / anti-EU and they really supported brexit. (By the by: this is why ken loach made a film about older northern white man, and not a film about uniting people with migrants.)
At 6am on the morning of 34 June when brexit won, Corbyn demanded the triggering of article 50, which is an advocacy of the fastest brexit track possible. He finally exposed his political position, but the Corbyn left are still largely in denial while also many of them are indulging themselves in british nationalism and doing so in an attempt of doing it guilt free, they have cuddly corbyn promoting a far right british nationalist project, so nothing to worry about!
Corbyn has gradually since June 24 2016 dropped defending migrants, dropped defending freedom of movement, and now he doesnt even talk about anti-racism anymore.
Brexit is a major political disaster and even sections of the ruling classes know this, hence Blair's comments. We have a similar fall out in the usa amongst the ruling factions over trump fascism.
Blair and Kenneth Clarke understand how disastrous brexit is, from the point of view of a traditional more stability-oriented ruling class faction, hence they are talking up against brexit racism, with Kenneth Clarke comparing in parliament Corbyn's leadership to the politics of Enoch Powell, a infamous far right Tory politician known for his anti-immigrant “Rivers of Blood” speech:
“If he was here he would probably find it amazing to believe that his party had become eurosceptic and rather mildly anti-immigrant in a very strange way in 2016.”