It's a good question, and the simple answer is that BoE QE and Corbyn QE are different things. They use the same words, possibly to muddy the water and sell the idea to the public, but they are actually very different things indeed and it's well to be aware of that.
Now if you'd like I can do another, much longer, post explaining what the difference is, but I decided to stick this up as a warning. You see, I got to wondering if anything similar to Corbyn's People's QE had been tried in recent global history and after a bit of digging about I found yes, it had. Not in any of the usual suspects like Zimbabwe, but in Ghana which began a programme functionally identical to Jeremy Corbyn's proposal in early 2013. And it's instructive to consider what happened next:
So, yeah. That's why it's a bad thing.
Hope that helps.