There already is dual electrification there.
That’s given me an idea - might be silly, but could the following perhaps work:
London Waterloo, Clapham Junction, Richmond, Twickenham, Feltham, Staines, Egham, Virginia Water, Sunningdale. Ascot, Martins Heron, Bracknell, Wokingham, Winnersh, Winnersh Triangle, Earley, Reading, Reading West, Reading Green Park, Mortimer or Bramley (skip stopping allows calls at Green Park) and Basingstoke??
Purely because; 3tph North Downs lines and an extra 2tph Waterloo services is going to put strain on the three terminal platforms at Reading.
If Reading - Basingstoke was electrified with third rail this would solve the issue of dual electrification at Basingstoke.
Reading West receives a direct London service, albeit a small one, and Basingstoke receives direct links to Bracknell, Ascot, Virginia Water and Staines.
Just like Waterloo to Weybridge via Chertsey when there are fast services via the SWML. Just like the “Ealing Broadway” advertised Paddington services from Oxford, the “Farnborough” advertised services from Dorset. It isn’t for extra services to Basingstoke from London because that would take ages (although probably not that much longer than the Winchfield and Hook semi fast stopper) it is for new direct links and connections, and to avoid overhead wire use at Basingstoke.