An super off-peak day return to London is £35.40 from Sway, £30.30 to Surbiton with no travel before 10:27. The fare to London rises to £40.40, no travel before 7:27, and £73.10 for any time of day. Single fares give few savings - the super off-peak day single, for example, is £35.30, or 10p less than the return.
For cheaper tickets, you have to book in advance - ie onto a single train - so we can't know for sure the cheapest available for you without dates. Tomorrow, for example, you could travel (one way) for £9 on the 21:34 departure, or £21 on the 09:27, changing at Brockenhurst. Further in advance there are still cheap tickets available all day - so on June 8th, for example, there are a number of £9 departures.
The best way to find cheap tickets is to use the websites of the train operators who use a certain booking system - I forget its name but others will be able to give you the full list. I always use
East Coast, and you can book any train service on here, but you may find a local TOC with the same booking system might offer extra discounts.