The cheaper ticket is not intended to be used via London
How do you know that and what bearing does this have on the terms of the contract?
PURPOSE OF THE NATIONAL ROUTEING GUIDE
The National Rail Conditions of Carriage require precise definition of the
routes that a customer may use for a particular journey. These routes are
known as "permitted routes". The National Routeing Guide enables users to
determine whether the proposed journey is via a "permitted route".
And the Conditions of Carriage:
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(d) The use of some tickets may be restricted to trains which take:
(i) routes passing through, or avoiding, particular locations; or
(ii) the most direct route.
These restrictions will be shown on the ticket.
Regarding Cross-London transfer, the Routeing Guide clearly states (referring to the routeing code found in the tables in the guide itself which is
not what is printed on the ticket):
If the routeing code is "LONDON", journeys include the cost of cross-London transfer either by London Underground or Thameslink services. In all cases the transfer points should be along the correct line of route given by the ‘permitted route’ map combinations.
So if you bought such a ticket, you have paid for cross-London transfer regardless of whether or not a Maltese Cross appears.
It goes on to reinforce the point that the Maltese Cross is
not the sole arbiter of the inclusion of cross-London transport by providing a particular example:
In some instances (particularly long distance cross country journeys) the Manual will show an "any permitted" fare but without the via London, Maltese cross symbol. Reference to Section C (the “yellow pages”) may show via London to be a permitted route for this journey and in such instances travel via London to include cross-London transfer would be permitted.
This has been the case ever since the Routeing Guide was introduced. By now the principle should be well-established and there would be little excuse if staff with control of ticket barriers on the routes across London were unaware. I did use such a ticket on the underground a few years ago without difficulty (on an "obvious" permitted route).
But that said, personally I would always choose a direct Reading to Gatwick train rather than take the cross-London route.