Airline and Itinerary

when applying for the 144 hr free entry does it matter if you are using the same airline or not? I originally bought a ticket from the UK to Beijing and return on British Airways but at the last minute realized my previous entry permit had already expired. So in order to still use my original ticket I will buy a ticket on Air China for Beijing to Hong Kong. I will apply for a new China Visa in HK and then return HK to Beijing stay for 2 weeks and fly back to UK.
Is there any problem utilizing two different airlines in this way?