Thanks for your comments. As someone who lives in the West Midlands, I have little to do with the conditions relating to the former NSE. Also that day I was travelling from Birmingham and had bought separate tickets Birmingham-Euston and Victoria-Gatwick and used my Oystercard on the Underground. The Birmingham-Euston ticket was an Advance but I had bought an Anytime ticket for Victoria-Gatwick as I did not know what time I would reach Victoria. I still make the point that a ticket marked 'Anytime' should mean anytime and as it was valid one day only it could have said 'after 9.30'
In that case, since Condition 14.1 of the National Rail Conditions of Travel state that:
... you may use a combination of two or more Tickets to make a journey provided that the train services you use call at the station(s) where you change from one Ticket to another.
your journey was from Birmingham to Gatwick, and hence did not therefore not both start
and end within the Network SouthEast area. As a result, had you mentioned your other ticket(s) and the resultant full extent of your journey, you should have been allowed to use your Anytime ticket on any Southern or other valid service you wanted to. (Whether you would have had this right honoured is an entirely different question!)
As an aside for next time - it's possible to get reasonably priced Advances all the way from Birmingham through to Gatwick and as long as you are at the station in time for your first train in your itinerary, you are perfectly allowed to take later-than-booked trains there or later on in the journey if you experience delays or cancellations which prevent you from travelling in line with your booked itinerary.
In a number of cases a combination of tickets will be cheaper than a through Advance, especially if you can accept a slower journey involving travel via Kensington Olympia or with the stopping West Midlands Trains service. Accredited/'official' sites such as
www.trainsplit.com are able to suggest such options and enable their booking all at once.