I have flown a *lot* of wine on BA over the years. Probably in the tons (ie 1,000s kg) by this point.
Almost all of it with fragile stickers and delivered to "special baggage" at check-in. Here's my experience of the outcomes:

Worst idea: putting bottles in your luggage. Baggage handlers operate under huge time pressure. If your bag looks like a regular bag, it will be treated like a regular bag and thrown/dropped at will. This is where I had the highest breakage ratio

Medium idea: leave the wine in the cartons/boxes it comes in from the winery. It won't have much padding but it will be obvious to baggage handlers that it shouldn't be roughly handled. Occasional breakage, but rare.

Best idea: 12 bottle capacity Styrofoam shipper (inside a cardboard box or "naked"), like this These boxes are indestructible, yet light and can be re-used on dozens of trips. I've never had a broken bottle (cons: you can only transport 750ml bottles, no magnums). I've also sent wine packaged this way around the UK by courier many times and never had an issue with breakage either.
12 bt in Styrofoam shipper will usually weigh in at 19-22kg unless you're buying absurdly heavy bottles (e.g. Sparking wine, Two Hands, anything from Argentina)