BR had a proposal to electrify the Cherwell Valley Line (Didcot to Banbury), a section of the Chiltern mainline from Banbury to Birmingham and the Leamington to Coventry line, this would have electrified Coventry as far as Didcot, then it is just the small bit at Basingstoke. Unfortunately the Conservative government (I don't want to bring in politics but it is relevant as this was around the time of starting privatisation) at the time did not go ahead with the proposal.Coventry-Reading - would allow the XC Manchester to Bournemouth service - surely one of the worst offenders for running diesels on electrified lines - to go electric, assuming suitable dual-voltage EMUs could be procured
It is on p17 (19 on the pdf) of this. Here is an image:

There is also quite a lot of other routes which would have been nice but never happened. On cost there is a table on p12 which shows what BR predicted it would cost, although they say the main issue was the disruption to passengers.
Planned under the now gone Electric Spine project.Nuneaton - Coventry
Already split on Sundays, you should just electrify all the way from Leamington to Nuneaton though.so you would have to split the service again.
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