If an when it does happen, it's unlikely to happen overnight.
...I'd imagine that Waterloo-Southampton would be a good starting point.
But that's what is so difficult.
What about all the other routes that overlap with that route?
There's Waterloo to Woking, Portsmouth, Alton, Basingstoke. It's a four track railway as far as Basingstoke so are you going to do both fast and slow lines, or are you going to have two separate systems for 50 miles? If you do the slow lines are you going to use dual voltage trains on the loop via Kingston? What about Chessington, Dorking via Epsom etc? There's Southern and SWT local services in the Southampton area too, so is the Southampton area to be dual voltage throughout - and of course most Southampton trains go to Weymouth or Poole so they'll all need to be dual voltage.
But if you are going to electrify to Southampton with OHLE to help out XC, why not go all the way to Bournemouth like XC services from Manchester do - it's the Newcastles that go to Southampton - but they need to be diesel for north east of BHM...
What are you going to replace WCML Pendolinos with - assuming the DfT allow them to go off the route they were bought for?