Your notice period is about time, not money. So if you hand in one month's notice, all that means is you telling your employer that you want to leave employment in one month's time. So if you're not being paid at the moment, unless you go back to work for the month, you will continue to receive no pay for the duration of your notice period.
Holiday is complicated, recent case law has indicated that employers should allow employees on sick leave to accrue and take at least the basic annual leave while on sick leave, and possibly carry it over if unable to take it.
However it's not all sorted out properly yet as there is conflicting legislation about things like carrying it over which needs to be ironed out. It was only during last year that this case law came up so it's extremely unlikely you are going to be able to persuade your employer to give you holiday pay going back any longer than that, in any case it wouldn't apply to past holiday years, only the current one.
Your best bet is to point out to them that recent case law indicates you should be entitled to holiday, then allow them to check into it, and make a decision about what they want to offer you, and then you can take it from there. As I said, it's complicated at the moment, and all about recent case law so there's nothing easy and concrete you can point them to as such.