its good that lender asked you to get ICB done before progressing .It gives you time to formulate about how it happened.
.1. Late payments are MISSED payments and if it was you had enough in Deposit but had let another account get low , that should be ok.
If it was a case you did not have funds elsewhere to cover payment then that is financial stress and will definitely not help your application..
explain what happened and say you didn,t understand (which you didn,t , of glitches on your icb)
From your short post, it looks like you had funds {substantial savings} even though you missed a structured payment ,so you should be OK .
Good luck.