This is covered by section 110 of Road Vehicles (Construction and Use) Regulations 1986, it seems. It is specific legislation for using mobile phones, hand-held, whilst driving.
There seem to me (not a lawyer, remember) two reasons an Apple Watch it not prohibited by that law.
1. The definition of "hand-held" which is "a mobile telephone or other device is to be treated as hand-held if it is, or must be, held at some point during the course of making or receiving a call or performing any other interactive communication function". I would not say a watch is "held" in any way.
2. The definition of mobile phone excludes "two way radio" (which is allowed), and that is defined as something to send/receive spoken messages (which an Apple Watch can) and "designed or adapted to operate on any frequency other than 880 MHz to 915 MHz, 925 MHz to 960 MHz, 1710 MHz to 1785 MHz, 1805 MHz to 1880 MHz, 1900 MHz to 1980 MHz or 2110 MHz to 2170 MHz". This means they actually specify the bands for mobile phone use, but left out the 2.4GHz bluetooth band that the Apple Watch uses!
I suppose in many ways it is the same as a bluetooth headset, which is simple allowed for mobile phone use in cars. The issue is more to do with sending/reading emails, and texts and crap on it whilst driving.
Interestingly they leave out some 4G bands too (2.6GHz), so all 4G phones that are designed to operate on frequencies outside those bands, even if not currently operating as such, are now a two-way radio, and so allowed. Actually, that would make any phone that does bluetooth a device designed it operate outside those bands (2.4GHz) and so a two-way radio. That is really badly worded double negative logic in the legislation there! Anyway, the Apple Watch only operates outside those bands.
Again, another pointless law that totally failed to keep track with technology.