I always believed Sunderland Corporation was the first to complete omo, from accounts in Buses Illustrated at the time, which I'm guessing now was 1972 or 1973, but that was more about replacing a fleet of double decks, including halfcabs, with new standee single deckers, from memory Daimler Roadliners, but I've never been to Sunderland, so it was only what I read! On the other hand, Hull Corporation could have been quietly introducing a fleet of Atlanteans/Fleetlines and gradually converting to omo, such that conductors were phased out by the end of 1972, so that may have been the first.
Other contenders not mentioned already might have been Maidstone Corporation, Brighton Corporation (the first to experiment with omo using halfcab forward entrance Leyland Titans), City of Lancaster and Barton Buses. Maidstone, though going into 1970 with only one remaining crew route, did however keep a couple of halfcabs for use on peak extras and schools duties, so it doesn't win.