It's really not that hard: remove height limits and parking minimums, per Yglesias in The Rent Is Too Damn High: http://www.amazon.com/Rent-Too-Damn-High-Matters-ebook/dp/B0.... Glaeser's The Triumph of the City is also good on this subject and discusses the UK more: http://www.amazon.com/Triumph-City-Greatest-Invention-Health.... This is a simple issue of supply and demand: rising demand in the face of limited supply means higher prices. Want lower prices? You need more housing or fewer people who want it. The former is easy to accomplish with century-old technologies, like steel and elevators.
FWIW, the London Plan currently contains restrictions on the maximum amount of parking provided:
table A4.2 Maximum Residential Car Parking Standards
Predominant housing type 4+ bed units 3 bed units 1–2 bed units
Car parking provision 2–1.5 spaces 1.5 – 1 space 1 to less than 1
per unit per unit space per unit*
* All developments in areas of good public transport accessibility and/or
town centres should aim for less than 1 space per unit.
Brazil has problems too - http://cities-today.com/2014/07/finished-brazils-largest-cit...