First thing to do is to ascertain why FedEx thinks that you as the receiver should pay for the delivery, rather than the sender. For FedEx to have a valid claim against you, you would have had to agree to be footing the bill at some point. If you definitely never did that, tell FedEx politely to get stuffed. If you did agree, then you'll have to pay and go after the hotel yourself - the background story is irrelevant for the issue between you and FedEx.
If you do have to pay FedEx, contact the hotel and ask them to reimburse you for the shipping costs. This is a "be firm and polite"-situation - since it was their mistake, they definitely ought to pay for it, but bringing an international law suit over £130 is just not going to be worth it.
The situation might be complicated, eg you may have signed something you thought said "I received this", but it actually said "I'm gonna pay for shipping". That wouldn't actually create the legal obligation to pay for it, but proving it might be near impossible. In this case, you could try arguing to FedEx that their agent mislead you, while contacting the hotel asking them for the reimbursement. Then go with whoever budges first.
Relaxed raised the possibility that FedEx might not be invoicing you for delivery, but instead asking you to reimburse them for custom duties they paid on your behalf. Since it is your stuff being send to you, it seems clear that you are liable for custom duties to HMRC, so if FedEx paid those for you, they'd indeed be justified in asking you for money. As above, it then is reasonable for you to ask for the reimbursement of the reimbursement from the hotel.