Do I have to notify the store?
Yes, probably. Not notifying the store would probably be considered fraud, specifically Fraud by failing to disclose information. The law says:
3 Fraud by failing to disclose information
A person is in breach of this section if he—
(a) dishonestly fails to
disclose to another person information which he is under a legal duty
to disclose, and
(b) intends, by failing to disclose the information -
(i) to make a gain for himself or another, or (ii) to cause loss to
another or to expose another to a risk of loss
Fraud Act 2006, Chapter 35
An example from a lawyer, which is very similar to your question:
An example would be where a person makes an insurance claim for a ring
that they believed had been stolen. They report this to their
insurance company and make a claim. They subsequently receive an
insurance payout of £15,000 for the ring. Following this they later
find the ring under the bed in their spare bedroom.
They have discovered that the ring was not stolen but lost and decide
not to tell the insurance company and then decide not to tell the insurance
company about it and keep the money (sic).
They are then guilty of an offence of failing to disclose information.
Quentin Hunt - Fraud by failing to disclose information
Note that the penalty for fraud is imprisonment for up to ten years (though you probably would not receive it).
Also note that the law is a bit vague on when exactly "fraud by failing to disclose information occurs. The act just speaks of "dishonestly failing to disclose information" and a "legal duty to disclose". In court the prosecution will have to prove that you acted dishonestly, and that you had a legal duty to disclose the information - the case law on that point is complicated. Usually the duty is more likely to be upheld if there is an existing relationship between the parties (such as in your case).
If I do, do I have to agree to them cancelling the refund?
Yes, you do. Once the store knows you have received the parcel (no matter how they find out), they have a right to get back the refund. Not paying back the refund is probably not a criminal offence (only a civil wrong), but the store may sue you if you do not pay.