It was Corbyn far more than Brexit.
According to the polling analysts the part Brexit played was twofold.
Committed Remainers were upset at the mixed messaging coming out from Labour throughout. This was largely every time a pro-remain/2nd referendum message was put out, which was in line with the position the majority of Labour MP's, Labour members and Labour voters wanted, someone from the leaders office leaked a contradictory stance. The media of course lapped this up. This confused much of the electorate, but for people who were highly Remain, it set them against the Labour Party, especially since, in May's snap election, they lent Corbyn their vote to block May's hard Brexit, only to be told that they were part of a huge majority in favour of one form of Brexit or another. Most passionate Remainers were prepared to hold their nose and vote Labour if that was still the only tactical chance of stopping a Tory, but some weren't.
In terms of Brexit voters, Brexit voters were much more passionate about Brexit. This meant that Labour leave voters were prepared to switch, especially since most were much more centrist and put off by Corbyn, whereas Tory Remain voters were far more frightened of a Corbyn led government that may or may not be in charge of a post brexit UK, than a Conservative led government in charge but delivering Brexit.
I'm pretty sure Starmer will win back former Labour voters, except some on the far left, and win over a number of floating voters and remain/decent/sensible Tories over the next few years as he builds bridges and concensus and Brexit and the nature of these very worst Conservatives comes out.