Would I qualify for the 144 h visa-free transit?

Yes, you are allowed to do that, but you should follow the next steps:

- To be eligible for 144 hour visa free transit in Guangdong province, your flight from UK to Shenzhen has to be a nonstop one.
- You will also have to book a ferry ticket from Shenzhen Shekou port to Hong Kong through CKS - Chu Kong Passenger transport company website. After a booking, you will receive an e-confirmation that you will print out and bring it with you.
- You will declare at check-in in UK that you will travel to Hong Kong via Shenzhen using 144 hour visa free transit and here you will present your ferry ticket.
- Upon arrival in Shenzhen, you will approach 144 hour visa free transit counter where you will fill out a blue form and also here you will again present your ferry ticket. After a short inspection, you will get a sticker in your passport and be allowed to exit the airport
- You will stay within the entire Guangdong province as you wish
- You will have to take exactly that ferry you have bought your ticket for
- To return back to Shenzhen you will cross the border, preferably at Lo Wu / Luhou border crossing where you will apply for a 5 day Shenzhen visa on arrival. This visa has a fee for UK citizens of 304 CNY and it is advised to bring that amount in Chinese cash.
- Keep in mind that with this visa you are allowed to stay only within the Shenzhen city boundaries.
- You can take a flight back to UK, but keep in mind that this flight has also be nonstop one.

That's it.

Is it now allowed to fly into Shenzhen and leave for HK/Macau?
I thought Shenzhen don't allow it when you're in transit.

It is allowed when you travel on 144 hour visa free transit and it is not allowed when you travel on 24 hour visa free transit. Since Mamoud intend to stay in Shenzhen area or wider, within Guangdong province, for 3 days, he will use 144 hour visa free transit and he is allowed to use Shenzhen airport to travel after to Hong Kong and/or Macau.