The Google results page has a built-in feature to detect the down arrow and move the focus to the next result. However, this only works with "instant prediction results" enabled. Could you check your setting?

https://www.google.com/preferences

Thanks for the quick reply, I've turned it on and in other browsers it solved the problem, but in FF it's still the same.

Can you tell whether it's working? In other words, if you type something like firefox pdf into the search box on the results page and pause, does Google display results without your having to press Enter or click the search button? Then if you press a space and add a word like adobe and then arrow down to the suggestion adobe plugin, does Google display results even before you do anything further? That's what I see which confirms to me that Google is use the instant results logic in the results. I do need to click the suggestion or otherwise finalize the query before I can press Tab to move the little blue triangle pointer into the results.

Now it works, thanks, The TAB part was missing in my sequence