Convert British OSGB36 easting and northing (British National Grid) to WGS84 latitude and longitude.
bng2latlong API is a free Geocoding API that requires no API key, is served over HTTPS and supports CORS, so it can be called from the browser.
Simple API to convert an OSGB36 easting and northing (British National Grid) to WGS84 latitude and longitude.
Details from getthedata.com.

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Yes. The bng2latlong API is listed in the Geocoding 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.
No. The bng2latlong API requires no authentication, so you can start making requests without signing up.
Yes. The bng2latlong API supports CORS, so front-end JavaScript can call it directly.
Yes. The bng2latlong API is served over HTTPS, so it's safe to use in production.