If they request it back you may send it back with property rights reverting to them (it’s a gift again) but legally there is no way to enforce it nor is there a request to get anything back For it (Ea. Money or other credit)
If there is no contract (Ea a purchase request/ intend) than anything a company Can send to a consumer is a gift.
I understand that there are restrictions to unsolicited goods, perhaps even a ban.
But an absence of contract does not make something a gift. Whether something is a gift or an offer to purchase or anything else depends on the facts, it's not implied.
So either there is a statute that says this case is legally treated as a gift or the item remain the property of the sender until the intention is clear.
Edit: There is indeed a law that makes it a gift (from EU Directive you mention, perhaps). See my previous comment above. This is indeed required because as explained it cannot be implied.
The thing that makes it a gift, is that A gift is the only allowed legal transformation that can happen. (Ownerships transfer is a transition in the legal sense). Ea. A company is required to always act lawfully and the only action open for unsolicited (=anything without a predefined base) package is to gift it.
A contract (=agreement to do something in exchange for something else, usually in paper but can be in any form even verbally) is needed before any transformation besides gifting.
This legal sense does not mean it’s still proper to send the package back if the company contacts you and pays for the shipping, but that’s not in law.
The detective I remember reading about during my ‘middle school’ studies (around 1998). I could be mistaken In it and if I am feel free to tell me. All I remember was that the directive made it so that all in the commons market must implement similar protections for Consumers regarding unsolicited mail and package by companies, not in small part to stop the extortion type of sale practice of the “free sample with overpriced subscription” (it’s why they switched to you having to request the sample)
Without such explicit law it wouldn't be a gift because it isn't the intention of the sender. These goods are sent as an offer. If you accept the offer then indeed a contract is formed, but if you refuse the offer then nothing happens, i.e. the goods remain the property of the sender.
That's why they enacted that law, in order to stop the practice altogether in one fell swoop as long as the public is aware of it (which clearly is still not really the case).
The Directive is from 2011. That's the one that was transposed in UK law through the Regulation I mention in a previous comment.
If you're sent something with a bill for payment then it seems to me that you are not entitled to keep it at all because the bill indicates that they are not gifting the items to you but expect payment for them. I.e. property rights have not been transferred.
You can of course keep the items and wait until being asked for them back (and then you obviously don't have to pay for sending them back) but that does not mean that you can keep them as in "they are yours to keep".
According to another comment it seems indeed fine to keep these unordered items in the US by Federal Law, but I don't think this is the case in the UK unless the intent is clear (and, for example, a bill clearly indicates what the intention is).
Edit:
Ah, I stand corrected. There is indeed a law similar to the US's one in the UK:
The Consumer Contracts (Information, Cancellation and Additional Charges) Regulations 2013
"(4) In the case of an unsolicited supply of goods, the consumer may, as between the consumer and the trader, use, deal with or dispose of the goods as if they were an unconditional gift to the consumer.”." [1]
[1] https://www.legislation.gov.uk/uksi/2013/3134/regulation/39/...