Counter-notice at work

Hello again - can anyone tell me with certainty how long the period is for giving counter notice? I have worked less than five years and was given standard three month notice but want to leave early.

Also, I realise that if I give counter notice , then I won't be eligible for chomage. BUT does the time work still accrue? So for instance, next time I have a job and am fired, the months I have worked here will still count? Or do I cancel it out by giving notice myself?
TIA