The register
The register lists John Hampden Grammar School in High Wycombe, Bucks as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Rating on the current register: Worker (A rating).
Companies House lists it as John Hampden Grammar School, number 07638999, incorporated 2011: 15 years of filings behind the name. Registered office: John Hampden Grammar School, Marlow Hill, High Wycombe, Buckinghamshire, HP11 1SZ, HP11 1SZ. By its SIC codes the business is in education.
A licence says an organisation may sponsor; it does not say it is hiring today. The way to find out is the same as for any employer: the careers page, the job boards, and a direct approach with a UK-style CV that says early that sponsorship would be needed.