You are entitled to your payment, but only if you are made redundant, if you quit first (leave early) you are not entitled to a payment.
You can ask your employer to agree an earlier date while still retaining your payment but they don't have to agree to this. You can also put in a written counter notice during the statutory notice period (the last 6 weeks of employment for you) stating you are leaving early and if your employer doesn't object you'll still get the payment, if they do object (in writing) then you have to stay until the end to be entitled to a payout.