In message , Clive D. W. Feather
writes
And if you were lucky you could get an eastbound District that was
reversing at Tower Hill or Mansion House.

Of course, if you are getting a train that is reversing (at Aldgate,
Tower Hill, Mansion House, High St Ken, Edgware Rd; as well as the more
obvious termini further out) that is another and rather direct means to
change direction...

The main sticking point for a Gatwick/Stansted transfer seems to be
getting onto/off the Circle from the Gatwick direction. Perhaps Waterloo
is the salvation here. Thameslink London Bridge, then Waterloo East,
Jubilee, Westminster, Circle. Does anyone know if the direct link from
Waterloo East to Southwark is stair-less, or will it require going via
the main station concourse?

[You can do Thameslink to Jubilee at London Bridge without stairs, but
it's a very long trek].
--
Roland Perry