Hairy Handed Fool, thank you for confirming that a Zone U1 (or similar) ticket is considered as an add on to a London Terminals ticket. Please could you tell me, are through fares such as sail-rail and bus links treated in the same way.
On to the original question. The ticket is routed any permitted. The National Routeing Guide states:
"If a choice of routes is available and the fare for the
journey is described as "Any Permitted" route or is unrouted, you are free to
choose any of the routes listed in the Guide."
http://www.atoc.org/clientfiles/File/RSPDocuments/instructions.pdf page 2
As Hairy Handed Fool has already pointed out, the passenger is not travelling on a direct train.
The London Group is a routeing point and Chelmsford is a related station to Shenfield and Witham.
http://www.atoc.org/clientfiles/File/RSPDocuments/routeing_point_identifier.pdf pages 14 and 39
We must now perform the fare check rule to determine which of these routeing points, if any, are appropriate.
A London Terminals-Chelmsford day single costs £12.20.
A London Terminals-Shenfield day single costs £9.30, this is less than the Chelmsford fare so Shenfield is an appropriate routeing point.
A London Terminals-Witham day single costs £17.30, this is more than the Chelmsford fare so Witham is not an appropriate routeing point.
The only routeing permission for London Group-Shenfield is CO.
http://www.atoc.org/clientfiles/File/RSPDocuments/permitted_route_identifier.pdf page 574
This allows:
London Liverpool St group-Stratford group-Romford group-Shenfield
http://www.atoc.org/clientfiles/File/RSPDocuments/maps.pdf page 18
Therefore, on the face of it, there is no mapped route allowing travel on HS1 out of St Pancras. However, it could be argued that as Liverpool St is a member of the London Group (as shown by the square point on map CO), which also contains St Pancras, and Stratford is a member of the Stratford group, which also contains Stratford International that the Liverpool St-Stratford segment of map CO also covers St Pancras-Stratford International. This would then give a mapped route as desired.
Whether the above argument is correct or not, which I am unsure of, it is a valid route anyway because of the following easement:
"Journeys on direct trains or taking the route of shortest distance or a distance longer
by no more than 3 miles are always following a permitted route."
http://www.atoc.org/clientfiles/File/RSPDocuments/nrg_detail.pdf page 9
As Bob has demonstrated, this easement allows this route.
My advice would be to write to South Eastern, citing the relevent section of the routeing guide and the distances provided in the National Rail timeable, and complain that the guard at St Pancras denied travel on a permitted route. This denies the right provided by condition 13 of the conditions of carriage.