No — water accounts can be closed after the event, but don't leave it any longer than you have to.
Tell your water supplier the date you actually moved out. If the property was metered and you're telling them late, you can still be charged for water used after you'd gone, so the sooner they have your dates the less there is to unpick.
Have a tenancy agreement or completion statement to hand as evidence.
Already been billed for a period after you left? Ask for the bill to be reviewed, and ask what's payable in the meantime while they look at it.