Would late payment to broadband (provider made mistake) affect my credit score?

Dear all,

Following MSE for years, I had been very careful on managing my credit score.
I recently switched to Natwest (£125 switching reward introduced by MSE), all went through just alright, except my broadband (Sky) direct debit.

Sky said I didn't make the payment, terminated my broadband, which I had to call and resolved it, causing me loss of broadband for 2 days. Sky also charged me late payment fees £7.50.

I spoke to Natwest, they claimed they informed all direct debit, even print out the information for me. Natwest said it is not their fault, and they cannot help further, it is my responsible to liaise with Sky.

Then I had to make several complaints, several calls to Sky for this problem. Finally Sky agreed to waive my late payment fee £7.50. I am not happy of "waive" the fee, because the entire incident was due to Sky didn't update my direct debit and cause unnecessary trouble to me (2 days without broadband).

My big concern is, would this late payment affect my credit score?