Ever since I've had my F the second fob did not work. Not a wise thing really. Much earlier I replaced the battery but without success. However, just today I visited
http://www.remotekey.co.uk/cars/MG/mgf-mgtf/faq.asp
and followed their advice of
"Open the key fob
Remove the battery
Press any button 10 ten times, and the same with the other button
Refit the battery or a new battery
Unlock the vehicle with the key in the drivers door lock, do not open the door
Press the right hand button lock button (the button with the padlock symbol or the dimpled button) on the key fob 4 to 8 times".
Lo and behold it worked.
By the way, holding the plipper under the chin while operating the lock or unlock button (the so-called Lucas position) really does work at quite a long range.