The register
Cimpress (UK) Limited is licensed to sponsor on Global Business Mobility: Senior or Specialist Worker and Skilled Worker. Its entry on the register dates back to at least 2026, and the organisation is based in London. The register records its rating as Worker (A rating).
Companies House lists it as Cimpress UK Limited, number 08708460, incorporated 2013: 13 years of filings behind the name. The registered office is at C/O Cogency Global (Uk) Limited, 6 Lloyds Avenue,, Unit 4cl,, London, EC3N 3AX, EC3N 3AX. Its filed activity puts it in business services. It has traded under other names before, including Vistaprint (UK) Limited.
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.