You are valid by:
a) direct trains - there are none
b) the shortest route - this is: Staines-Virginia Water-Chertsey-Woking-Farnborough-Basingstoke-Southampton-Bournemouth-Dorchester South
c) By routes shown in the National Routeing Guide, available at:
http://www.atoc.org/about-atoc/rail-settlement-plan/routeing-guide
These are calculated as follows:
Staines is a routeing point.
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf page 68
Both Dorchester stations are members of the Weymouth Group.
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf page 19
Routeing permissions for Staines-Weymouth Group are as follows: LONDON, WW, WX, and WX+WE.
http://www.atoc.org/clientfiles/File/permitted_route_identifier.pdf page 910
As your ticket is routed 'Not London' we can discount the London routeing permission.
WW gives:
Staines-Cherstey-Woking-Brockwood-Farnborough-Basingstoke-Eastleigh-Southampton-Weymouth Group (a duplicate of the shortest route)
Staines-Cherstey-Weybridge-Woking-Brockwood-Farnborough-Basingstoke-Eastleigh-Southampton-Weymouth Group
http://www.atoc.org/clientfiles/File/Maps.pdf page 122
WX gives:
Staines-Feltham-Twickenham-Richmond-Barnes-Clapham Junction-Wimbledon-Surbiton-Woking-Farnborough-Basingstoke-Eastleigh-Southampton-Weymouth Group
Staines-Feltham-Hounslow-Barnes-Clapham Junction-Wimbledon-Surbiton-Woking-Farnborough-Basingstoke-Eastleigh-Southampton-Weymouth Group
http://www.atoc.org/clientfiles/File/Maps.pdf page 123
WX+WE gives:
WX: Staines-Feltham-Twickenham-Richmond-Barnes-Clapham Junction-Wimbledon-Surbiton-Woking-Farnborough-Basingstoke-Salisbury-Westbury
WE: Westbury-Castle Cary-Yetminster-Weymouth Group
WX: Staines-Feltham-Hounslow-Barnes-Clapham Junction-Wimbledon-Surbiton-Woking-Farnborough-Basingstoke-Salisbury-Westbury
WE: Westbury-Castle Cary-Yetminster-Weymouth Group
WX: Staines-Ascot-Wokingham-Reading
WE: Reading-Newbury-Westbury-Castle Cary-Yetminster-Weymouth Group
http://www.atoc.org/clientfiles/File/Maps.pdf pages 114 & 123
Note that those routes generates by maps WX & WE, ie those going via Westbury, Castle Cary and Yetminster, are not permitted with a Gold Card discounted ticket as they leave the network area.
Your proposed route via Salisbury, Romsey and Southampton is not permitted.
--- old post above --- --- new post below ---
I can see no reason why Yeovil would not be a permitted route though as it is inside the network area and clearly permitted by this set of maps.
Unless I am missing something obvious, the section between Salisbury and Yeovil is not shown on any of the maps indicated by the routeing permissions.
--- old post above --- --- new post below ---
Salisbury - Southampton Central via Romsey does not appear to be on a permitted route unless there is an easement somewhere I have missed. Same applies to Clapham Junction, or Brighton.
Clapham Jn is permitted on map WX. I agree with you on Romsey and Brighton.