Direct answer
HMRC says to stop student-loan deductions from the first available payday after the stop date on the SL2; that means the first payday on which it is practical to apply the notice.
The notice, current HMRC guidance and payroll software control. An employee request alone is not authority to stop; this is not payroll or tax advice.
Source checked 2 August 2026: HMRC employer guidance, updated 6 April 2026.