Seeing that most Bakerloo trains originating at Elephant & Castle don't run the full length of the current route (terminating at Queens Park or Stonebridge Park)... why not think outside the box?
There are still two seldom-used platforms at Charing Cross, from when the Jubilee Line was diverted to Westminster... if you're going to build more tunnels anyway to make the extension, why not bore tunnels to access those platforms (from the south) and terminate some 'new branch' trains there ? Passengers wanting a through journey from the new branch to, say, Baker Street or beyond, would need to change at the previous station, though...
The idea here was to extend the Bakerloo Line from Elephant & Castle to Lewisham and then onto Hayes/Beckenham Junction, the seldom used platforms at Charing Cross are a rather seperate matter. Various ideas have been mooted for getting them back into use but that's as far as it's ever got.
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Very unlikely to happen now according to the just-published public consultation. I'd be amazed if we ever saw Bakerloo line trains beyond Lewisham.
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Or along the Catford Loop, where (unlike at Lewisham) there is plenty of spare capacity and currently only 2tph actually serving the stations.
When the ELLX was under debate one of the options included a Victoria - Bellingham stopper twice an hour. I could imagine Clapham Jn - Bellingham being a similar prospect.
The Catford Loop line is also used by fast services and obviously the capacity becomes more limited with Victoria to Lewisham services joining at Nunhead. Increasing services to 4tph, at least as far as Bellingham, really should be a priority.