The police generally won't be interested unless a person has been missing for at least 48 hours.
However, that's only a guideline. If, for example, an estate agent suddenly went missing during the course of his/her work, showing clients around houses, (as in the case of Susie Lamplugh) the police would almost certainly launch an immediate investigation. On the other hand, if a homeless 'drifter' failed to turn up at the hostel where they'd been staying, it might be several weeks (if at all) before any form of investigation was carried out.
For further advice, phone the National Missing Persons Helpline on 0500 700 700.
Chris