Very disappointing news. Arguably, the key paragraph in that Beeb report is a quote from Jack himself:
"However, I've had this injury for a long time. I'm at the very, very end stages of the [recovery] process and to step back on court into best-of-five-set tennis so soon just doesn't seem like a smart decision right now for me and my tennis."
And as Jonathan Jurejko opines in his analysis at the end, better safe than sorry.
Bad news indeed. On the plus side tough, Jack has just the 200 points from the AO that he can't defend and his next drop is Doha on 23rd February. So hopefully this withdrawal won't set back his ranking too badly.