Milton Keynes is currently served by the Look East (West) sub-opt from Cambridge.
Yep - though AIUI this is because of the cable system implementation? I think that ITV1 London and ITV1 Anglia are both available - but am not sure if both versions of BBC One are provided?
The history behind the South region is pretty complex and goes part of the way to explain why there's so much overlapping and a few anomalies. Originally I think, BBC South stretched from Dorset to Kent and included London.
Not true in News terms.
Originally there was the South regiona out of Southampton - and the London and the South East region, which got
regional news programmes produced by BBC Current Affairs at Lime Grove. This was in the era of South East at Six in Nationwide, South East in 60 Minutes, and London Plus.
However in some regional opt-out slots where other regions got short local news bulletins, BBC London and South East viewers got other stuff instead.
The original London and South East region (referred to as South East on-screen) included the BBC Oxford region (now a sub-opt of South Today), the current BBC South East region (now a full opt from Tunbridge Wells) and BBC London (now a full opt from Marylebone High St)
BBC London and South East moved from Lime Grove to Elstree in the late 80s, and just a bit before this the BBC created Macro-regions.*
The South East region was created and included Oxfordshire, Greater London and Kent, Surrey etc. The most recent big change was when "South East" became Kent/Surrey only (from Tunbridge Wells), "London/LDN" was formed and produced from Marylebone High Street and the Oxford transmitter was reassigned to the South region and a sub-opt was created for Oxfordshire and surrounding areas.
In the late 90s a review of the London and South East area was undertaken - because a single BBC service was covering a very large area. The results of this were that BBC London became a separate operation, BBC South East for Kent and Sussex became a separate operation, and BBC Oxford became a sub-opt out of South Today.
This was phased - with BBC Oxford splitting away first, then Newsroom South East moving to the new BBC London premises (it continued as a very basic CSO for a month or two) before South East Today and BBC London News (aka LDN) launched.
* BBC Macro Regions
The original macro regions in the late 80s were:
BBC South (which then included BBC South West, West and South), BBC South and East (which included BBC London and the South East, and BBC East)
BBC Midlands (BBC East and West Midlands)
BBC North (BBC North West, BBC North East and Cumbria, BBC North)
Eventually in the early 90s the Macro regions were re-jigged again, creating :
BBC South (BBC South West, BBC West, BBC South and BBC London and South East)
BBC MIdlands and East (BBC East Midlands, BBC West Midlands, BBC East)
BBC North (same as before)
Some regional shows were produced on a Macro regional level. BBC South and East used to produce a dual-region show called "Weekend" - which came from the BBC East studio in Norwich (at the time this was unused because Look East came from the Newsroom) but featured reports from as far away as Kent and Oxford. Fiona "GMTV" Philips did the travel on it - with scary hair and make-up...