All EU nationals have the right to work in the UK.

If you make your application, then the Settlement Resolution Centre should issue a Certificate of Application (CAO) prior to making a decision on your application. You can use this CAO as a proof that you submitted your application and it also proves that you have right to work. EU nationals should not be required to provide this until 1 January 2021 onwards.

Gov.uk provides a service for employers to check whether their employees have right to work. This link will provide a share code that your employer can use to check whether you have right to work in the UK. Your employer will need the share code and your date of birth. The code is valid for one calendar month and can be shared directly with your employer via the website.