I was in London a few month ago and had to pay something like £4 to take the tube 3 stops. So either prices have dropped, I got screwed or your numbers are off.
You got screwed. The cash single fare is about double the incremental fare using an 'oyster' card.
Yeah, in London currently, did a double take when I saw the difference between Oyster and standard fare. The standard fare is absurd, whereas oyster puts it on par with NYC (and has the very nice feature of acting as a la carte until you reach a maximum for the day, at which point it effectively becomes a day pass).
Yep, you got screwed. Next time pay the £3 for an Oyster card, and save a TON of money. Whether you pay trip-by-trip or a travelcard for a day/week/etc, Oyster is WAY less expensive.