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/...