Transdiffusion's always a good source to start with.
AFAIK, never seen any evidence that ATV London mounted a local news operation and presumably the ITA at the time didn't feel weekend coverage was an obligation as such (despite what companies such as ABC and Southern had managed to do)
There is this table, taken ad verbatim from the 1963 ITV yearbook, which maps out what each region was - or wasn't - doing at the time (the concept of a nightly regional magazine was very much still in its infancy)
itv1963.transdiffusion.uk
Of course, there would have been at least some local elements to ATV's output in London - Police 5 got its start, for example. And remarkably, there's a surviving clip of one early edition in the Dutch public broadcasting archive.
www.youtube.com
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YouTube.
To the same degree, Rediffusion's local programming record was poor but not necessarily non-existent.
They did have bespoke weather forecasts with (ex-Squadron Leader) Laurie West, but as Transdiffusion argue, the company appeared to think ITN more than adequately cover London in its bulletins.
'Three After Six' aside, there was also a weekly magazine programme for a while called Londoners, hosted by Ludovic Kennedy.
transdiffusion.org
Of course, even after Thames took over, they didn't really have a local newsroom operation in the traditional sense until the demise of 'Today' - and I suspect, the IBA's overtures leading up to the 1980 franchise round - forced their hand.
John Freeman, then chairman of LWT, also spoke out against the IBA's calls to boost local news at weekends but that's another story entirely.