there are a few DNOs I believe that will now allow 4kW under G83, sadly not the one I have to work with!
The G83 requirement is based on the output of the SYSTEM, not the panels, which is why a 4kW set of panels with a 3.6kW inverter is fine. the DNO should take the lower output of the two as the system output. by the same token if for some bizzare reason you put 3.6kW of panels on a 4kW inverter that would also be ok under G83.
Multiple installations in the same post code (which is what I meant by immediate area, although I don't know if it could extend beyond that to any house served by the same transformer) do require notification, for the same reason as larger scale installations, in order for the DNO to assess if the local network is being 'overloaded' with back feed for the same rather feeble reasons they have to approve installations over 4kW.
As such if you, say, did multiple installations on the same street (like a certain firm me and yellowvanman know!) the DNO could come back retrospectively and ask for the systems to be switched off and ask for payment from someone (you or the householders!) to survey and possibly upgrade the electrical infrastructure.
Strangely doesn't appear to be a problem in Germany!!