Its been a while, and I've now found a solution to this.
ForceBindIP
http://www.r1ch.net/stuff/forcebindip/
Download it, stick it in the Windows\System32 folder.
Find the GUID of the Network card you want to use (via RegEdit) and run this command...
C:\Windows\System32\ForceBindIP.exe {5CBB6FC0-3C9D-43C4-A166-0CB41387F7E8} "C:\Program Files (x86)\Mozilla Firefox\firefox.exe"
Bingo, firefox is bound only to the Wireless card.
Why? Because the wireless network at work is un-restricted, wired is restricted.
So when I want to get to a blog entry that Google promises to solve all my problems, then its time to fire up Firefox.