start at the beginning!
do you have a full birth certificate? if so, it should have your parents addresses on it. using this address, go to the local studies library in the central library and have a look in the electoral rolls...you can check each year for that address - at least you will then have an idea of how long they lived there.
if they were there for any length of time, it might be worth going to the old address and asking if the current residents have any info on where they moved to - might give you a base to start searching the electoral rolls with (which is a long and laborious process!!)
but, probably wont get far with that as people tend to be cautious when strangers turn up on thier doorstep!
next stop id try would be the phone directory - theres a chance they may be listed....i have rung hundreds of numbers trying to find relis, and it usually works.
also, if you knew where they worked, you could try there - they may have kept in touch with colleagues who may be able to help.
lots of leg work im afraid, but its a start.
lovin life in my new house!