Great Western Coffee Shop

Any time day single, Richmond to Reading via London, £24.10
Off peak day single, Richmond to Reading via London, £22.70
Any time day single, Richmond to Reading, any permitted route, £14.80

Can anyone explain the existence of the first two fares?

Includes Underground?

A normal journey from Richmond to Reading would not be via London terminals. At least the two fares give people the option of doing this without having to pay separate fares

The third fare is routed 'Any Permitted'.

To confirm permitted routes one can consult the National Rail Routeing Guide. Doing this you'll discover that one of the permitted routes for Richmond to Reading is LONDON. That means you can take any permitted route from Richmond to London Terminals, make a cross-London transfer by Underground, then take any permitted route from London Terminals to Reading.

There is one small problem though. The 'Any Permitted' fare doesn't include the Maltese Cross (✠) printed on the ticket evidencing that an included cross-London transfer is encoded and can be made. This is an error. However, the Routeing Guide is the final arbiter of permitted routes. If it says a route is permitted then it is, regardless of how the ticket is encoded. Any error on the rail industry's part is their fault. A passenger is entitled to take a permitted route as detailed in the Routeing Guide. Expect TfL gateline issues though.

Should this error be pointed out to the TOCs responsible for setting the fares between Richmond and Reading? Probably not. They'll just amend the 'Any Permitted' fare to 'Not via London' and make the '✠via London' fares '✠Any Permitted'.

There is no concept of 'normal journey' when deciding permitted routes. The arbiter is the Routeing Guide.