Just thought I’d see if anyone else is having the same strange problem with the WiFi on their iPhone after the 3.0 update.
Essentially, WiFi works fine after the phone has been freshly booted (i.e. right after a restart) - however, once it has put itself into standby mode it will no longer download data over a WiFi connection after the phone is turned on again. It remains able to find the WiFi network, but simply refuses to download data over it.

Have tried restarting my phone and changing the WiFi security from WPA to WEP, but to no avail

You can try it on the open area its work because whenever you are inside the any building then the signals of WIFI becomes weak.

Some times when you are going to be much inside in the building or some where then the signals of WIFI becomes weak.