British passengers, flying London to Shenzhen, to Hong Kong to Shenzhen to Seoul

Well, you cannot travel on 24 hour visa free transit: London - Shenzhen - Hong Kong.

You can do it under 144 hour visa free transit and that means that you are required to stay at least 24 hours and 1 minute in Guangdong province area before you can proceed to Hong Kong. You can proceed to Hong Kong by ferry, but you will have to buy a ferry ticket through CKS - Chu Kong Passenger Transport company website before your departure from UK and print it out. Your departure to Hong Kong has to be slightly after 24 hour of stay so that you become eligible for 144 hour visa free transit. Also, you will really have to take exactly that ferry you have bought your tickets for.

After your stay in Hong Kong, you can enter Shenzhen, but you cannot use any visa free transit scheme, but you can do it only by applying for a 5 days Shenzhen visa on arrival at designated border crossings. The price for this visa for UK citizens is 834 CNY. Please, be at the border crossing on time in the morning to avoid the queues. Visa offices start operating at 09:00. The best border crossing for this purpose is Lo Wu / Luohu that you can reach by train from Hong Kong or Shekou port in Shenzhen that you can reach by ferry from Hong Kong. Shekou visa office opening hours: 9:00 - 13:00 & 14:30 - 16:30...

One more detail... You are allowed to take a flight from Shenzhen to Seoul, but have in mind that this flight is not allowed to have any additional landing within mainland China on its way to Seoul.