Marking is generally in VL contracts - the hourly rate (supposedly) covers that time. So you probably do need to do the marking. However, I think you'd be reasonable to say that as you have visitors and no space, you can't start on the work until 2nd January.
But really try not to load this onto another hourly paid lecturer: it's above her pay grade. She's probably under the same pressures as you.
Escalate to the Director of Education of your department.
Try to word your email so you don't land the module convenor in the shit - hourly-paid people should not be convening modules, but this is the state of UK HE (one of the best exports we have, but not because of government support ...)
Say that the key for the exam materials is incorrect, and the time you'd set aside for marking is past, and that you are now on annual leave until 2nd Jan. Ask that the correct materials be with you then, and give the Director of Ed a reasonable time for your delivery of marking - if you went at it for 2 8 hour days, would that clear it? You'd be able to offer delivery of marking for 5th January, which is pretty reasonable actually.
We have a 3 week turnaround at my place, including 1st & 2nd marking, and administration of marks, before they're released to students (which I think is institutional bullying) but bank holidays etc don't count, so you'd still be only a few days over the 21 working days.
Good luck! This is the state of UK HE, folks.