I don't get sick pay, and want to use my holiday to cover it.. Can I?

Strictly speaking no. If your line manager is happy for you to take leave after the fact that is between you and them, but the purpose of the holiday leave regulations are to ensure that employees have sufficient time away from work to be rested, and should normally be taken in blocks of a week or two weeks. Most employers usually require 4 weeks notice for a weeks holiday, and by their nature leave after the fact cannot do that. If you are signed off for a week or more you can apply for Statutory Sick pay, it is not much and you do not get anything for the first 4 days, but it is better than starving.