Three years later, I found the game!
It WASN'T an arcade game, it was a NES game called "Rad Racer".
You can see from the screenshot on this page that I was correct in remembering the driver looked like a Lego man!
http://www.hardcoregaming101.net/rad-racer/
Memory is a strange thing - I could have sworn that I had replies to this thread, but it seems no one replied! Nevertheless, I thought I would post the answer, just in case anyone wondered.
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