Get an Oyster card
Not having an Oyster card is a tax on tourists. A zone 1 single costs £4 without a card, but only £1.80 with one. The amount you pay is capped at the price of an equivalent travelcard, so unless you get one with your rail ticket, it's guaranteed to save you money.
A card is a £3 deposit and doesn't expire. You can also use it to open our door.
From UK =
Get the Oxford Tube from the High St to Victoria Station. It's slightly cheaper than the train, and includes free Wifi and power sockets at your seat.
Walk to Victoria station for the District line, and change at Whitechapel for Hoxton.