I can't see how it would be valid via Horsham and Three Bridges in the same journey as that would involve doubling back through Littlehaven, unless an easement permit it.
Bear in mind though that doubling back is allowed when using the 3 mile rule.
Using the mileages that ATOC supply to booking engines, the shortest route from Littlehaven to London Terminals appears to be 35 miles 30 chains to Vauxhall, via Horsham, Dorking, Epsom and Wimbledon. The other route via Three Bridges, East Croydon and Streatham Common is 1 mile 25 chains longer, at 36 miles 55 chains. Of course once you get to Vauxhall it is permitted to continue to Victoria as there are no other stations in between that aren't London Terminals (this bit might be wrong; see below).
If we start a journey along the second route with a double back to Horsham, that adds twice the distance from Littlehaven to Horsham (i.e. 2x 1 mile 6 chains) to the total mileage, which brings the total mileage Littlehaven - Horsham - Littlehaven - Three Bridges - East Croydon - Streatham Common - Vauxhall to 38 miles 67 chains.
That is 3 miles 37 chains longer than the shortest route! ATOC specify that booking engines should apply a margin of error to the three mile rule. If the margin of error was half a mile (40 chains), then this route would be allowed. So it's quite open to interpretation...
I haven't checked with mileages from the GB Rail Timetable. That would be an interesting comparison obviously.
Edit: I am confused about where Vauxhall is. Not sure if you can get from Vauxhall to Victoria or not. The same reasoning applies though if you choose Victoria instead of Vauxhall as the closest London terminal; in fact the difference in distance is then less than a quarter of a mile over 3 miles.
Edit again: I don't think the fact that we are using Vauxhall as the closest terminal is of much consequence. I think it would be a bit unenforceable to say to a passenger who had reached Clapham Junction that they now could only go to Vauxhall rather than Victoria, just because they had that double back to Horsham at the start of their journey. It is certainly very complicated though and hurts my head thinking about it. Maybe one for John@Home.