Because the direct debit has already been set up to go out today. The money willl have effecytively been set aside at midnight last night. I think this is the normal practice. You will probably find the T s and Cs say 24 hours notice is required for cancelling a DD. Anyway if you did cancel it you may find that causes problems with whover you should have paid- they may levy a charge.
If your employers have paid you late they should compensate you. When should you have been paid?
Which bank is it? Given what the bank has told you, you may be able to pay cash in today to cover the DD. Even if you have to pay someone �10 to lend you the money until Friday it's cheaper than paying the �38 DD charge.