The register
The register lists The Cookaway Ltd in London 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 The Cookaway Limited, number 11570053, incorporated 2018: 8 years of filings behind the name. The registered office is at 93 Grand Drive, London, SW20 9DW, SW20 9DW. Its filed activity puts it in hospitality.
What the licence tells a candidate is that the door is not locked. Whether it is open this month is a question for The Cookaway Ltd's own careers page and the job boards, and the answer changes with the season and the order book.