It all depends on where you are, how many vehicles want to park, and what the road and pavements are like.
Now parking outside of my house on the pavement isn't a problem at all, as the pavement is roughly 15' wide, so you can easily park two cars fully on the pavement outside our house (next to the wall), and another 4 in front of the neighbours wall and still have an 8' wide pavement for the cyclists to swerve around the mothers and their prams.
However I suspect that you are correct in that it is a problem in many areas, and that is going to get worse, all thanks to "Two Jags" Prescott. Why would it be that lovable John Prescott can be having an impact? Well the office of the deputy prime minister has responsibility for planning, and PPG13 (Planning Policy Guidance Note No13) is explicitly about forcing a modal change in transport through planning restrictions.
ABD page about Two Jags policies that force others not to have more than one car (or in some cases to have no car at all):
http://www.abd.org.uk/ppg13.htm
Corrected link (ABD on is out of date) to review of PPG13
http://www.odpm.gov.uk/index.asp?id=1145481