Unfair late payment terms

Hi All, apologies if this has been a topic already answered but cant seem to find an answer anywhere.

We have recently entered into business with a another limited company which contains a term with regards to late payment:

If payment is not made within 5 days from completion a 15% charge will be added.

The work has totalled in excess of £3000, so that would be a rather extortionate charge if say paid 1 or 2 days late.

We have not paid the invoice for the works late, as we are disputing that the payment terms do not explicitly state either calendar or business days, and the invoice does not contain a due by date, so we have interpreted the payment period to be 5 business days and have made the payment in accordance.

My main concern however is what's the legal recourse for unfair/extortionate late payment fees? The law is clear that anything below statutory late payment charges is less than a substantial remedy and are void. However I can only find a clause which says parties are subject to agree their own terms to constitute late payment?

Is it lawful and fair for a party to display such a fee that deviates from statutory interest by way of being much larger?

Thank you for your quick reply:)

I think that's definitely reasonable for the courts to potentially agree unfair terms - just makes me slightly worried that there is a lower cap on the law for unfair terms but not a ceiling for the substantial remedy legislation.

Nevertheless I often obsess about these things too much and cant see a small business taking another small business to court over a 2 day payment difference on an extremely short payment window as well!