Fortunately my apartment block has a 24 hour concierge, so hopefully it shouldn't matter what time he decides to turn up! I've had a text from a delivery driver though, which sounds promising...
So onto the next question, can I expect some Avios from BA as compensation? I couldn't really justify going and buying clothes/toiletries etc since I was on my way home anyway, but it's been a bit of a pain to be without everything for 4 days.