As indicated above, any probationary period associated with the new job may lead to the back withdrawing the loan offer.
I was in a similar situation myself. Took the new job and didn't tell the bank about it. They somehow found out anyway so I had a lot of explaining to do one Friday afternoon when they rang me and quizzed me over it.
In the end I successfully argued that the new position was even more secure than the previous one as the new company were more established, but it was a close call.