I was in exactly this situation couple of months ago, flying JNB-LHR in F, and bag was never loaded. I don't live in London and was due to fly out 2 days later so spent £300 on clothes. Slightly long story but I think the details are interesting for you:

- Claimed via Amex Plat insurance (AXA) first but was denied because I was returning home. I actually had other flights on that PNR so it wasn't the last flight on the booking but they rejected it on the basis that the flight in question was to my home country (despite my registered UK address being 10 hours away from Heathrow!).

- Claimed via BA online and followed up by phone few days later where they confirmed they had approved claim and initiated bank transfer.

- Received email few days later saying they were rejecting the claim and no explanation given. So I replied asking for one, and they replied again that it was being rejected and gave no further explanation.

- I called back multiple times and was given different reasons for rejection, including that it was because I was returning home and because my travel insurance had rejected it so they would too (!!).

- I finally lost my patience and asked to speak to a supervisor who said all the many reasons were valid (although couldn't point out where the rules were stated) and that I was possibly committing fraud by claiming from AXA and BA. I only went to BA after AXA rejection but I did not provide the Amex insurance details in my BA claim so they figured that part out themselves. I didn't include the details because I was uninsured in my view given that AXA had rejected the claim but maybe they thought I was trying to hide something.

- She was rude and not willing to listen and asked me to pursue CEDR. I gave up at that point.

It seemed completely unreasonable to me given that I had already been told it was approved and they clearly didn't have a set rulebook they were following. I didn't play the DYKWIA card, but let's not forget I was a ticketed F passenger!