Praise be to Allah.
It is not permissible to buy goods through the system mentioned, because the bank stipulates a penalty in the event of late payment. That is stated clearly in the adverts for this system on the bank's website on the Internet, which says:
To avoid a penalty for late payment, it is essential to pay on the due date.
Stipulating a penalty for late payment is blatant riba, whether the bank takes a penalty for itself or distributes it to the poor. A statement to that effect was issued by the Islamic Fiqh Council, no. 133(7/14), during its fourteenth session in Doha, in which it says: “If the purchaser/borrower is late in paying instalments and misses the due date, it is not permissible to oblige him to pay anything additional to the debt by means of a prior condition or otherwise, because that is haraam riba. End quote from Fiqh al-Mu’aamalaat al-Hadeethah by Dr. ‘Abd al-Wahhaab Abu Sulaymaan, p. 571
This is in addition to what the transaction involves of other problems. If the bank is going to buy the item from the seller, then it is not permissible for it sell it until it has moved it from the store where it was bought to another place that belongs to the bank.
If the bank is not going to buy it from the store, which is what appears to be the case based on what is said in the question, as the purchaser is going to pay part of the price to the original seller, and all that the bank is going to do in this case is pay the rest of the price to the seller in the form of a loan to the purchaser, and charge interest or riba, as mentioned in the question, then this riba is the basis of the transaction, regardless of whether interest is charged for the delay in payment mentioned or not.
To sum up: it is not permissible to buy goods through this system, because of what we have mentioned of the stipulation that a penalty be paid in the event of late payment, which is a riba-based condition which it is not permissible to accept, even if the purchaser is determined to pay on time; and because of other matters that are contrary to sharee’ah that we have mentioned.
And Allaah knows best.