My understanding is that the defence mechanisms that have been put in place since the last crash are far more robust, but I grant you that the express train that is bearing down on us may well overwhelm everything, and make Brexit look like a summer picnic in the process. The BoE is nominally independent, but I think you'll find not quite as much so in practical terms. The government, after all, appoints the governor, and the current incumbent has been behaving as though he were actually a part of the government, and very much not independent. However, the UK is still threoretically in a better position to respond to crisis than, say, the French, Greek, Spanish, Irish or Italian governments, because their hands are fully tied both by their membership of the Euro, and by EU/ECB defict rules, whereas the UK is in charge of its own fiscal levers. The ECB, under the current rules, and already with QE wound up and negative interest rates, has absolutely no fiscal ammunition left it its bunkers, and the combination of a stonking world recession and Brexit could easily prove decisive for the end of the Euro. This is all widely acknowledged amongst economists, I'm not just making it up.
Anyway, we'll all see in due course. It just does look to me as though the EU is going to be willing to throw its best client to the lions at the very moment that the global financial cesspit is about to explode in its face, all for the sake of a dated and pointless ideology to which it is fatally and inseperably wedded.