An MOT due date is the expiry date of the previous MOT certificate on your vehicle, it is your responsibility to have a valid MOT certificate if you drive on the road. If you drive without an MOT certificate for your vehicle, you could receive a hefty fine and invalidate your insurance as well as it being potentially dangerous.
You can get an MOT test on your car any time before the current expiry date, but if you want to preserve the MOT renewal date and get it before the expiry date, the earliest date it can be carried out is one month minus one day of the expiry. For example, if your existing MOT runs out on 4th November, the earliest date you can have your MOT test and keep the same renewal date for next year will be 5th October.