Definitely not South Africa. Sounds a little like a "Relaxed" Australian. Time for google!

What i found.......

"Now for the record, the Geico Gecko has been voiced by Kelsey Grammar (the stiff English accent), Richard Steven Horvitz (the voice in the Kung Fu Fighting spot), and Dave Kelly (the relaxed British-Aussie accent)."

Kelsey Grammer was the first acording to two websites but Jake Wood seems to be the main guy now. Thats him below. I see no resemblence.