C
Your forum name appears to be your real name, I recommend that you change it, see;
www.benefitsandwork.co.uk/guides-for-claimants/faq/forum If you fail to attend the assessment or cancel the appointment with no intention of remaking it then your ESA will stop from that date.
If this is your first appointment then you can request a second date "more convenient for you", which will likely give you at least several more weeks of payments, wait until a few days before the appointment to contact the Assessment Provider.
Then you will have to decide whether to close your ESA yourself or leave it to the DWP, the latter may result in a recoverable overpayment.
Gordon