I am amazed that this idea is still being pursued.
Replacing the Third Rail would be a massive waste of money - yes, it's not ideal, but neither is overhead electrification. There is little need for more than 100MPH running on the third rail system, particularly given the frequency of stops on most routes.
Of course, you can't replace the odd bit of third rail equipment as it becomes life-expired, you have to replace the whole system over significant sections of track.
In my view, there will always be much better things to spend the available money on than to replace one OK, but not perfect system of electrification with another.
Electrification of the entire Manchester and Leeds suburban systems, plus the Welsh Valleys, would be a start. After Pacer replacement, of course.....and much more.
The Basingstoke - Weymouth line has severe electrical capacity limitations the substation equipment is rapidly becoming life expired although west of Bournemouth is new than the Basingstoke Bournemouth section it is limited in power and the equipment was put in by
BR▸ to a "budget". It cost ^1M to renew a substation and even more to build new additional ones, it is possibly more economic in both money and time to re-electrify the the line than to renew / enhance the existing.
The Brighton Mainline also has major power supply limitations which will limit the length and frequency of trains.
Both these routes have roiling stock that is ac / dc compatible the stock that is not can be cascaded to other routes