Labour campaigned and voted against Brexit shouting this would happen. "Project Fear" as it was called. But now they pretend like Brexit has nothing to do with it... it's just the torries fault apparently.
The Labour leader at the time of the referendum was luke warm about remaining at best. So much so I doubt he voted to remain despite what he said. He had a long history of criticism of the EU.
The stated position of the labour party, and what they campaigned for, was Remain. At the time, there were many people like you saying one thing about Corbyn while he said another. Nobody liked Corbyn, so he surely must have been a Brexiteer! Despite him not having made Eurosceptic comments for many years.