BTW, I've been at the opposite end, also in UK. I was wrongly accused of picking up someone's Amazon package, the police got involved, they showed up at my door and said something like "could you check again in your apartment if you maybe by mistake have picked up the package".
I suggested to the police to investigate the common areas cameras in the building to see who the Amazon delivery person left the package with, but I don't think they bothered since it probably involves a search warrant.
And that was it, nothing happened. Amazon eventually reimbursed the other person and ate the loss.
Paperwork exists for a reason.
In my view at fault in these cases is the delivery company, they are in a hurry and don't bother doing a proper job. If they would be forced to eat the cost, this wouldn't happen anymore. Basically they are outsourcing their job to the police force.
Basically evidence.
If the police can't take evidence and solve a crime then fuck 'em.