I booked 2 rooms in a hotel for dates in February that allowed cancellation free of charge and then proceeded to cancel these rooms because I noticed they were offering the same rooms for cheaper on another part of the booking page. Unfortunately this second booking was a non refundable booking. The rooms were not clearly advertised as being non refundable and I only found this out when I got an email today saying my credit card wasn't valid. I usually have no trouble with this (I gave them my debit card details and not my credit card). They say that if I don't update the card details to a credit card instead of a debit card within 24 hours my booking will be cancelled and that I may be charged. The card that I have has zero funds in the account. I am just wondering can I be charged when there isn't any money in the account? All third party transactions are blocked by my bank.
Most booking websites display terms, such as being non-refundable. They may not be prominently displayed, but usually enough to covers laws. The fact that you were distracted by the discount you got and didn't read the terms carefully is not usually grounds for a waiver.
Can they come after you for the cancellation fee? Yes they can, because you entered into a contract with them for the booking. Will they come after you? Not likely as the legal fees outweigh the fee due. But that said, they could try to bill your debit card at a future date in hopes that it becomes funded (something they could legally do up to the date you booked for).
Or if you want the rooms, you could simply give them credit card details and be done with it.