| Comment | Another poster has linked you to a night latch (colloquially known as a Yale, even if it isn't even branded as Yale), but those automatically snap into locked when you shut the door.
The way you describe it by locking it on the inside by turning something on the inside and locking by key on the outside sounds more like a thumbturn euro cylinder, which is a standard eurolock like the ones you find on every UPVC door, but one side is key and one side is a little knob.
https://www.toolstation.com/era-6-pin-euro-thumb-turn-cylinder/p12588?store=CV&utm_source=googleshopping&utm_medium=feed&utm_campaign=googleshoppingfeed&gclid=CjwKCAiAudD_BRBXEiwAudakX_4rpWLrGbQe_EJdGoTidJpz1fyD8CbM9bSDo6gzE5L8SIpp4hGmiBoCQScQAvD_BwE
If that looks right, then you will probably also need one of these sashlock cases that you fit into the wooden door then fit the eurolock cylinder into the case:
https://www.toolstation.com/euro-profile-sashlock/p11830?store=CV&utm_source=googleshopping&utm_medium=feed&utm_campaign=googleshoppingfeed&gclid=CjwKCAiAudD_BRBXEiwAudakX2wxcS-nMArwqMh37wVNwsU0M6pX3rh-Fe0xqXfFPdiqhNGNd2q1fhoCYI4QAvD_BwE |
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