In my experience I have found that mortgage lenders make all kinds of promises about how they may list payments but if the payment is due on the first and if it isn't available in the account on this day when they go to take it it is automatically marked as a late payment, often as a missed payment. A late payment is supposed to be where a payment is missed but is paid within 7 days of the date, a missed payment should be marked for any time after this. Unless I have numerous clients that are lying to me (and it could be that they all are) I would say that irrespective of when you made the payment you will have a late or missed payment marker against your file.
When it comes to your remortgage it could cause you a problem as it will immediately flag on the credit score and because it is such a recent payment that has been missed it will concern the lender just that bit more. I would imagine that if you have any way of proving to them that it was a genuine mistake (can you get a printout identifying the mortgage as a personal loan and also a copy of your bank statement for the date showing the funds in the account) that most lenders will be happy with this. After all, if you had the money in the account at the time of payment then it would have been paid.
Most lenders will allow a one missed/late payment within 3 years and this could save you too but my main concern would be that the missing payment is so recent....but that could also be your saviour too.....
.....As this is so recent, it is going to take your mortgage lender a few weeks to update your credit file and so I would advise (for more than just this reason) to see if you can book your new mortgage product with a lender now. It will take a few weeks for your fuile to update and this may mean that you have your new mortgage offer before it hits your credit file and nobody will know. Most mortgage products can be booked up to 6 months in advance of the end date of your current mortgage and the product will not start until your current deal has expired so this would mean that if you had a mortgage that ended on 31 July 2012 you could effectively book a new remortgage product right now and it would just start the new product on the 1st August (after yourt penalty had run out.)
The other reason I would suggest that it may be wise to remortgage now is that over recent weeks with all the European turmoil the lenders mortgage rates (not national interest rates) have been steadily rising to the point that I would say that are 0.50% higher than they were 2 months ago.
I don't think I would be panicking about your situation but I do understand that it is a worry, after all it was you that cancelled the DD and so the fault does lie with you. But it is an honest mistake and not a missed payment through lack of funds and I would like to think that the lenders can dig deep into their black souls and try and find a bit of compassion for you in this case.
Good Luck!