I would suggest editing the OP to remove address, phone numbers etc.
If I read the emails right (30th April) they are offering to send it to Birmingham but not Manchester? That might be your best result depending on the value of the item.
Shocking customer service I agree, however to immediately reply to them about your intention to “make you annoyance public” probably hasn’t helped your cause. In my day to day work I generally am not at my best when people try to threaten me. They probably get hundreds of lost property items each week so it’s easier to say no than help.