If an employer asks for proof of your Student visa work rights, you can direct them to the information published on the university's website, as this can be accepted as evidence under the Employer Right to Work Guidance. The university does not provide individual letters confirming when students can work full-time.
You can show your eVisa, which includes your work conditions, alongside the university's academic calendar and term dates to demonstrate when you are permitted to work full-time. Your CAS letter showing when you have gone past the expected end date of your programme can also serve as confirmation. For more information, please refer to the university's guidance on working in the UK during your studies.