Can I fly London - Shanghai - Dubai - London

Yes, of course you can because your itinerary is definitely eligible for 144 hour visa free transit in Shanghai. Anyway, I hope that your flight from London to Shanghai is a nonstop one and not through Dubai!

By the way, 72 hour visa free transit has been replaced in Shanghai by 144 hour visa free transit a couple of years ago. Also, you should use correct terminology because it is not "72 or 144 hour transit visa", but 144 hour visa free transit, so there is no visa at all.