For some reason, that website isn't offering off-peak Zone 4 travelcards, which are available and cost £8.90 (£7.70 on Oyster).
OP, if you tell me your exact itinerary then I can figure out your cheapest fare options.
If you'll be spending more than a couple of days in London, you probably want to get an Oyster card, which is cheaper and more convenient. You can buy a Pay as you Go Oyster at any tube station for a £5 deposit, and you can return the card at any tube station and get your £5 deposit refunded, plus any remaining credit on the card.
That's hardly any in-london travel at all. Pick up an oyster card, top it up with 20 quid and cash it out at a station when you're leaving. In any case, you will never be charged more on your oyster than you would have been for an equivalent travelcard, while you might be charged significantly less.