The register
The register lists Thesqua.re 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 Thesqua.RE Ltd, number 06687220, incorporated 2008: 18 years of filings behind the name. Registered office: Unit 3 Barrel Yard, Vinery Way, London, W6 0LQ, W6 0LQ. By its SIC codes the business is in hospitality. It has traded under other names before, including House of Modern Living Limited.
What the licence tells a candidate is that the door is not locked. Whether it is open this month is a question for Thesqua.re Ltd's own careers page and the job boards, and the answer changes with the season and the order book.