Cheapest way to travel on tube

I personally would go to Waterloo with that super off-peak CDR: you can split tickets at Basingstoke in theory if your train stops at Basingstoke, or Woking, and thus save further. I wouldn't bother for the effort and get a one-day off-peak Travelcard from Southampton, change to the Jubilee, get off at Wembley and walk. On the way back you have until the last train to get from Waterloo..0105 or the earlier 0005 MX? Journeys started the day before are covered by the ticket.

The cheapest way to get to London is probably via Southern, using their various cheapo offers, as it is after 1030, but the Victoria - Southampton trains finish earlish SuX and don't run at all SuO. I think unless they have cancelled them trhe cheapest ticket is £10, or the next one up £13.50. To that you have to add the LU element.

And to explain a bit further, an "Open" return is valid on any train, a "Cheap Day Return" is valid on all trains except those of interest to people commuting into London (ie morning inbound, early evening outbound), and a super off-peak return is the same, except the periods it isn't valid are longer. The nationalrail.co.uk Journey Planner can show you which if you click the "More Fares" option, but as I say, both your trips are very much off peak.

I agree..get the YP Rail Card if you qualify.

I have been trying to work out the cheapest way to get to Town for years! In fact the best miles per £ was from my then local station, Swanwick, which you could go:

SWANWICK-CENTRAL-WATERLOO
SWANWICK-FAREHAM-WATERLOO
SWANWICK-FRATTON-WATERLOO/VICTORIA
SWANWICK-HAVANT-WATERLOO
SWANWICK-VICTORIA VIA HOVE
SWANWICK-LONDON BRIDGE (ONE PER DAY)

which was in the case of via Central, an extra 1/2 hour of train for the same price as direct from Central! I used to prefer however to go via the Victoria train to Havant, thence by fast Pompey to Waterloo and buy a nice Danish Pasty and coffee from the friendly buffet staff. I gather that this anomaly as far as Porchester still applies.

However, getting back to today, on Southern from Central - Victoria, the cheapest is the Day Save unlimited travel at £10 plus £1 for each accompanied child, or the Pricebuster at £13 is impressive value.

I may have misunderstood, but Travelcard tickets to places outside London don't exist. You're meant to buy a Travelcard then a separate "Boundary Zone 2" (if you had a Zones 1-2 Travelcard) to Guildford extension ticket.