Public transport is cheap and abundant, competition keeps prices down for restaurants and shops, and there are a lot of free events to keep you busy.
The main expense is in the accomodation, which most people in their 20s combat by sharing houses in undesirable areas. (This is a problem UK wide though as they have managed to keep our housing bubble inflated unlike in the US.)
London is expensive for tourists though. A ride on the Heathrow Express, a few nights in a 3* hotel, and a spin on the London Eye would be enough to make Zuckerberg wince.