Yes! I have exactly the same problem. On my Windows 7, 64-bit machine the issue is exactly as you describe. My broadband provider is also Orange.
I have a Windows Vista 32-bit machine and that works fine. On my 64-bit machine I have tried disabling my anti-virus (Avira), reinstalling all drivers, changing encryption settings on the router (as suggested by Orange) and also the wireless channel (again suggested by Orange). None of this works at all and I can't stream most media. Oddly, if I go to Soundcloud, it works fine wirelessly. It is very, very odd.
I get the same style results on the iPlayer diagnostics page. Connected via Ethernet cable I am also okay. Does anyone have any ideas at all? I am now going to try this machine on other wireless networks and see what happens.