Hmm...
I’m not entirely sure about this, OP. The story feels a little too convenient in places.
FWIW, my concern is less with the delivery team and more with the situation your daughter was placed in (by you). Most people are aware of how deliveries work, especially for large items that require two or more people to carry. A time slot is always given, and yes, they can arrive early, late, or bang on time.
Leaving the timing aside, I’m surprised you didn’t think to keep your phone on hand that day, even just in case. It’s the kind of precaution most of us take because you never know. Similarly, giving your daughter a heads-up about the delivery would have been a sensible and useful thing to do. Again, you never know (as we've seen).
Also, it seems you opted not to pay the extra fee for delivery up to your third-floor flat, which meant the item was supposed to be left at ground level. From the delivery team’s perspective, how could they be sure that your daughter wasn't the one who arranged the delivery, changed her mind about where she wanted it delivered, and now owed them £60 for the change in delivery agreement? Even if she said she wasn’t, they had no way of knowing for sure as she's legally an adult.
Of course delivery staff don’t typically insist on payment before completing the delivery. They’re expected to bring the item to the agreed room/floor first. So no, they wouldn't have insisted on the extra payment before delivering to your 3rd floor flat. That would have been unprofessional.
It’s possible they’ve encountered situations where customers tried to avoid charges, which might explain why they insisted on payment, which they're entitled to by the way. It's not really their fault that you didn't make proper plans for this delivery.
As I said, I feel for your daughter. It must have been frightening just having to handle something you failed to prepare her for. The way this unfolded suggests she was caught in the middle of a plan that wasn’t fully thought through. I can see how the “intimidated by two men” angle could be used to strengthen a refund claim but the company may be well within their rights here.