It reminds me of a common misconceptions:
- the Super Bowl is watched by a billion people worldwide, when that is only the potential audience and the real figure is closer to 100 million, almost all of whom live in North America.
- how the wedding of Prince William and Kate Middleton was supposedly going to draw 2 billion viewers, but it was probably more like 300 million.
Another factor which makes me skeptical is that Top Gear only draws about 5 million viewers in the UK on a good day, or less than 10% of the country's population.
For Top Gear to draw 350 million viewers worldwide, that would mean it is drawing 5% of the entire world's population - a remarkably small drop-off, considering how many people in the world don't even own a television, let alone be interested in a show in a foreign language with many specifically British cultural references.
I have to stress the fact, that the real version of the claim is:
The British automotive show is seen by 350 million viewers in 170 countries every week.
This is what I'm skeptical about. (Not that, in overall 350 million people have seen the show.)