Although it's definitely part of Hertfordshire, I think Watford should fall under the remit of London.
Why I hear you cry? Well, it's within the M25 for a start, joined onto London without countryside in the way, it's on both the Overground and Underground, and to me it "feels" London more than it does Hertfordshire.
Maybe all non-London places within the M25 should follow suit. Staines, Epsom, Dartford, Loughton, Chigwell.
What can you see as being the arguments for and against such a move?
That's an interesting one. If you look at it purely in terms of public transport, then there's a very good case for transport in Watford to be run by TfL, since it is the natural terminus for a fair few London metro services. However, local authorities are about much more than transport, and I'm not too sure how well matched London and Watford are in other areas.
I'd question your assertion that it's joined onto London: There's an almost continuous band of countryside stretching around the South of Carpender's Park and Bushey, so it's pretty hard to travel between Watford and London without going through at least some countryside. However, I'll give you that it's a narrow band. I'd also point out that, if the aim is to put the London boundary roughly where the built up area ends, then Dartford, Staines, and Epsom would all have much stronger claims than Watford to become part of London, since they are all much more strongly part of the London built up area.
Overall, it's quite tempting to suggest that a more natural London boundary would include all four areas: Watford, Staines, Dartford, and Epsom. That would certainly be good for transport. And I suspect it would benefit those areas more generally, since it would mean they would be governed by a Mayor and and Assembly that has somewhat greater powers than do most local authorities (and which seems to be reasonably competent too).
Doing that would have a few wider political implications as a side-effect: By increasing the population that is part of London, it would strengthen any arguments for devolving more powers to the London Mayor/Assembly. It would also slightly increase the Conservatives' chances of taking control of London in elections (although, given the rate at which inner London seems to be moving leftward politically probably only slightly). It would certainly mean that those areas would change from being under almost certain Tory control to at least an even chance of Labour control at the county level. I don't think that should be part of the arguments though.
Offhand the only argument I can think off offhand against expanding the boundaries would be that London is already the biggest local authority in the country, and this would make it even bigger. I don't think that's a particularly strong argument though, since population-wise it's only a small % increase.
In the end, it probably hinges on the extent to which people in those areas feel culturally/economically associated with London, and how great the shared interests are.