I did some research too- on a government site I wouldn't quote ACAS, it's just an advisory service which is quoting the law, as opposed to the law itself.
As you said you have to work somewhere a month to be required by law to give a week's notice. Soo my idea is:
"As you are aware I only joined ASDA living on <insert date> and therefore I am not yet required to give you the statutory one week's notice and therefore I tender my resignation with immediate effect"
Is it a bit lawyery? If so sorry. It's also a bit brazen though but you are miserable working there hon and cannot afford to have to go back sanity wise.