Power of attorney automatically lapses upon the death of the person who granted it, so it's completely irrelevant as to what you now can, or can't do, in relation to your father's estate. However, if your father's bank account is still open, absolutely anyone is free to pay money into it.You should seek to get the account closed as soon as possible though, in order to prevent standing orders and direct debits being paid out unnecessarily.
If your father left a will, it's now the executors of his estate who're empowered to handle his affairs. If he didn't leave a will, you'll need to seek letters of administration to sort out his estate (unless his estate was very small).