Depending on the type of student you are, different things will happen to your email access.
Taught Students (UG/PGT)
Your email account will change to the Alumni email 'For Life' scheme. Any emails which were in your mailbox will still be there after this change.
For more information on Alumni email please see Knowledge Base Article: Office 365 - Alumni Email 'For Life'. If you opted out of Office 365 this service will not be available to you.
Research Students (PGR)
You will lose access to your on-campus email account once your grace period is over. Any important personal emails will need to be backed up or forwarded to another account before your grace period ends.
As a research student you will have access to an 'Alumni email for life' account however this will be with a brand new mailbox which will not contain any of the information which was previously in your email account.