Why this matters
Workers and incumbent employers sometimes confuse the immigration step (new visa approval) with the employment law step (notice period). The two are separate, and getting them out of order delays the worker's start date with the new sponsor and creates avoidable conflict.
When the notice period begins
Under UK employment law, a notice period begins from the point at which the employee formally gives notice, not from the point at which a new visa is approved. If a worker hands in their notice on a given date, their contractual notice period starts on that date.
Statements from a current employer that "the notice period only begins once the new visa is approved" have no basis in UK employment law and are incorrect.
Working full-time for the new sponsor
A worker who is changing sponsor cannot work full-time hours for the new sponsor until:
The new visa application has been approved by the Home Office.
A new right to work check has been completed by the new sponsor confirming the worker has permission to work in the sponsored role.
In the period between starting the visa application and approval, the worker can in principle continue under their existing sponsor's arrangements (including supplementary work for the new sponsor up to 20 hours per week, subject to the supplementary employment rules).
Practical recommendation
Workers caught between conflicting positions from current and prospective employers should consult ACAS or take independent legal advice on their employment rights. The sponsorship side and the employment side need to be handled in parallel.
Government guidance: https://www.gov.uk/handing-in-your-notice and https://www.gov.uk/uk-visa-sponsorship-employers