Many refrigerated products (Bacon, ham, black pudding etc.) have this warning on the packs. I assume this is due to being packed in a protective atmosphere. Provided I wrap the remainder securely in cling film or Saran wrap and use it before its "Use By" date, will it still be safe to eat past that time? Or is this warning purely about food quality (e.g. drying out in an open packet in the refrigerator)?
This is trickier than the case of "use by"=safety and "best before"=quality.*
If there's an additional "use by" date, as there often is, that shouldn't be exceeded, but if you open the packet on the day of purchase there can be a big gap between the two. This warning is often combined with "packaged in a protective atmosphere", and that gets complicated. Modified atmospheres in food packaging (Wikipedia) can have different effects on microorganisms that cause detectable spoilage and that are harmful. Restoring to the normal atmosphere changes that again. So it might be possible for the manufacturer to set a longer safety period and a shorter quality one - but they don't.
So I can't advise you to stretch that time in case it's safety-related for that specific product and timescale, even if I might be a little incautious myself. If I'm planning on keeping this sort of stuff longer after opening than it says, I freeze it. All but the cheapest (water-filled) ham freezes well, but you can't separate it frozen so I put non-stick sheet in between and can defrost a couple of slice at a time. I haven't cooked bacon in years, but have frozen that too in the past.
* In UK terminology, though others tend to be similar.