It appears that when some third-party Bluetooth headsets are paired with the iPhone and active (a phone call is in progress), Wi-Fi-based browsing in Safari is not possible.
A poster to Apple's Discussion boards, Rehan Ashroff, writes:
"This is what I am experiencing so far. Scenario 1: connected to WIFI; start phone call; audio source: bluetooth headset. Cannot browse Web using WIFI, pages dont load.
"Scenario 2: (connected to WIFI; start phone call) except this time I am using the built in speakerphone and not using a Bluetooth headset, and can surf the web using WIFI while … Read more