"I am certainly not following this rational on wake separation...Perhaps some views on the thought or approved process."
There are two separate separation standards being discussed here - the 2.5nm (then Reduced Separation in the Vicinity of the Aerodrome) is completely separate to the wake vortex issue. Subject to certain conditions, the closest that UK radar controllers were permitted to get aircraft was 3nm - whether they were following, passing, crossing etc. Any closer than 3 miles was a loss of separation. At some point it was determined that, as discussed by others more knowledgeable above, 3 miles could be reduced to 2.5 miles for aircraft on final approach to LHR. As an aerodrome controller, you can easily get aircraft much closer than 2.5nm anyway - imagine two departures rapidly turning onto different tracks, or an inbound following something visually etc. The judgement falls to the aerodrome controller to visually assess if the separation is safe and appropriate, and as hangten says, if we can safely issue a landing clearance at a useful stage to the second aircraft.
Wake turbulence is a completely separate issue and overrides any other reduced separations.
The final approach spacing will be a combination of the above, plus any adjustments required either by the tower (eg availability of exits, braking action, departures to go in between arrivals), weather (eg tailwind, icing conditions requiring a/c engine anti-ice hence higher approach speeds) etc etc.