Ask an Immigration Solicitor. Get an Answer ASAP.
Good afternoon, I am Lawyer Ak and I will be assisting you today.
You will be able to apply for the graduate visa before expiry on 31 October however if you leave the U.K. whilst application is pending it can be withdrawed.
You will need to enter before 27 September to make application for the graduate visa.
Coming back on 24th September will not be an issue as long as you have valid visa.
It was a pleasure assisting you today. Kind