Hello kesannah,
I'm not sure that with the records that I have I can be very helpful. The divisional number of 188K is the number that officers were issued when working within a division, in this case division K. Unfortunately these numbers weren't unique to a person, so when officer 188 moved to another division the next officer would inherit this number and so on.
Also I have had a look for a Joseph Watson and can't find him in the Registers of Leavers - which only go as far as 1947. I've had a quick look on the Alphabetical Registers of Joiners and couldn't see a Joseph Watson in there either - it covered 1911 to 1933. Is it possible that he served in the City of London Police?
The best thing I can recommend is to contact
The Met Collection (email on the linked page) and see if they can do a look-up in their records - as they have some which cover officers who joined later in the 1900s and have more records indexed. If you know when the officer with 188K served that should help narrow it down for them.
Sorry I can't be of more help

, BarnabyP