The other problem is that the WLL is an important freight route
across London, and cannot sustain a very frequent passenger service
without loss of freight paths. Also, where do your trains terminate?
Paddington would be possible eventually (post-HEx), I suppose. I doubt
that
there is the terminal or line capacity further east.

Sure, throw them on the circle/district/metropolitan/hammersmith and
city line

Coudn't you terminate underneath Paddington, next to the Bakerloo
line? Or even carry on on a tube tunnel across Marylebone, to Euston,
and KX? Or perhaps take a northern view, via Finchley Road, Camden
Town, Highbury and Islingon to Liverpool Street?

OK the tunneling would be expensive, but it would allow the majority
of tube traffic to circle London without going into zone 1.

Bear in mind that from (West Kensington) the Cromwell Curve to South Ken the
Circle/ District already has the Piccadilly underneath. With the advances in
technology it wouldn't be an additional burden on the existing setup either.
Paul