Visa free used twice in a roll

I plan to travel from London to Hong Kong, and stay in Beijing for 144 hours, I will stay in Hong Kong for 4 days, and come back to London again through Beijing, staying again in Beijing for 144hours. Would this be a problem?
Also, what I explained above is the itinerary, but I plan to buy two roundtrip tickets, one from London to Beijing, and another another ticket from Beijing to HongKong, so I will have my confirmed tickets, but in a way these will be bought separately, would that be ok?