Photograph the listing before you bid on a bca car.
Photograph or record the sale if possible. Download assured and condition reports. Photograph auction sheet in 'Your Purchases' post purchase.
Notify them immediately if a car arrives missing a spare key/service book/V5. Dont just email claims notify the auction and cc in auction manager and sales staff as well.
If I buy a car with a spare key and it doesnt arrive then they are ordering me a new one or giving me the go ahead to get one organised. I can stomach the hassle of getting a new key coded.
Theres no such thing as insurance that pays out easily so you have to get the facts to back your case and be persistent until you get satisfaction.
On the baldy tyres, an insurance company could argue that you are sending them a random picture of another car. Pull out your phone take a 30 second video, full view of the car and reg "This is KK19OOO, purchased from BCA yesterday with an assured report stating 5-6mm across both front tyres". Get a close up and use a tyre depth gauge if you have one to then show the car that arrived as only 2-3mm as stated.