British Citizen Travel UK to Hong Kong

No, unfortunately, this is not possible because Hong Kong and mainland China have separate immigration systems and 144 hour visa free transit applies only for mainland China area. However, there is one relatively complicated, although doable solution...

You can fly from Hong Kong to Guangzhou (the entry by air is the only solution if you want to enjoy 144 hour visa free transit in Guangdong province) by a nonstop flight and exit from Shekou port in Shenzhen to Macau by ferry. Like this, you would be eligible for 144 hour visa free transit because your itinerary would look like:

Hong Kong - Guangzhou (in reality the entire Guangdong province) - Macau

This is an itinerary that satisfies the basic criteria of 144 hour visa free transit. You should have just a several more requirements:

- You will have to buy your ferry ticket even before your departure from Hong Kong through TurboJet ferry website
- You will have to print out that ticket and have it with you at hand
- You will really have to take exactly that ferry you have bought your ticket for

When you arrive in Macau, you can just proceed back to Hong Kong immediately. I know that this is not of some particular help, but at least you can think about this presented option to see if it has some sense for your needs.