There are two separate elements with a one-way street. There will be a NO ENTRY sign and passing that the wrong way is "failing to comply with a traffic sign" Then there will be a TRO, specific to the location, which will spell out in some detail the extent of the one way bit including where it finishes. There will be advisory signs (rectangular) and there may be mandatory signs (round) the latter being at junctions to direct traffic to turn the right way. There's chapter and verse in the relevant bit of the Traffic Signs Manual which I have linked to before.
In short: a NO ENTRY sign may or may not indicate the start of a one-way street, but a one-way street won't start without one (often two, of course.)
Chapter and verse here: https://assets.publishing.service.gov.u ... ter-03.pdf
see p 16 COMPULSORY AND PROHIBITED MOVEMENTS
The signs in this section generally give instructions regarding manoeuvres that must or must not be made. Positive signs tell drivers what must be done; prohibitory signs indicate a forbidden manoeuvre. They cover both junctions and the sections of road between junctions.