It will be interesting to see what London Live do (wink wink) ... as to the London edition of the Radio Times - it actually covers the whole SE .. I doubt they'll print a special version just for the parts of Kent & Sussex covered by the new show. Just print both programmes in the one edition.
I thought the London edition just went out to the Carlton/LWT area (ie London & Home Counties), and that Kent and Sussex had the South (Meridian) edition, which, the last I time I saw it, had both South Today and Newsroom South East in it, for the benefit of those in Kent and Sussex who receive Meridian ITV and BBC South East; then Newsroom South East would simply be substituted for South East Today. Anyone who gets the London (Carlton/LWT) edition will be in the BBC London Live region, and unable to see South East Today properly (i.e. me).
Sorry if I'm labouring this point, which isn't terribly important anyway!