UK Companies House Data from the UK government.
UK Companies House API is a free Government API that requires OAuth authentication, is served over HTTPS and has unconfirmed CORS support.

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Yes. The UK Companies House API is listed in the Government category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The UK Companies House API uses OAuth authentication, so you need to register for credentials before making requests.
CORS support for the UK Companies House API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The UK Companies House API is served over HTTPS, so it's safe to use in production.