In the probationary period you are on a week's notice period so you can either turn up on your first day and hand in your notice or you can inform your employer right now to give them a fighting chance of filling your position as soon as possible.
Assume this is linked to your other thread about deciding to move back to the UK?
Your contract should describe the exit criteria for the probationary period. Many companies have a probationary period of 3 months where either side can terminate without cause. Check the contract and align to that.
If you do that it shouldnt impact you later, unless you find yourself applying to the same company again back in the UK (for example if it were are large Swiss bank). The company internally may have your hire period on record and not hire you again. This doesnt prevent you applying to others though of course.
These things happen during the probationary period.
You can always resign for XX personal reason, it's not like they will ask if you already knew before signing the contract. Or even that it was not a good fit on your side. Honestly, it's not uncommon that people leave during probationary period, it exists for a reason. The important thing is that you can justify it if a future employer asks why you left so soon.
is it 80% in terms of hours or are the days always full time? maybe there was a communication problem and you could renegotiate (money maybe, if they are understaffed)
in any case if that is their situation and it's some kind of service industry job, I would guess they will be happy to have had you during the festivities even if you leave afterwards