Single tickets from London Waterloo to Honiton at £12 a trip are readly available on your dates. Advance purchase only - online or at a staffed station
An open return (buy on the day) from Appledore to Waterloo East via Ashford is £29.40. Via Haywards Heath (ie Eastbourne/Lewes) is £28 but takes over an hour longer.
http://www.firstgreatwestern.co.uk/ is as good a place as any to buy them
Megatrain
http://www.megabus.com/uk/index.php is slightly cheaper for London Honiton - same trains, less frequent
The advance tickets - both normal and megatrain - will go up in price if you don't book now.