Hong Kong to Shenzhen Airport to UK

No, you will have to apply for a 5 days Shenzhen visa on arrival at one of three designated border crossings. You can use 5 days Shenzhen visa on arrival, but you cannot use a high speed train from Hong Kong to Shenzhen. In reality, you can use just three border crossings: Huanggang and Lo Wu (Luohu) keeping an eye on their opening hours: 9:00 - 16:30 and Shekou if you plan to reach Shenzhen by ferry from Hong Kong. Shekou opening hours: 9:00 - 13:00 & 14:30 - 16:30. I suggest you to use Lo Wu, but to arrive there before 09:00 to avoid the queues.

Important detail is that UK passport holder have to pay 834 CNY for Shenzhen VOA due to reciprocity.

After you have reached Shenzhen, you can take a flight from Shenzhen to any country, but please have in mind, your flight out of Shenzhen is not allowed to have any additional landing within mainland China of any kind.