I'm holding UK passport can I do SIN-Shenzhen-HKG-SIN?

Yes, you are allowed to do that, with the exception of train. Train is not allowed as a legitimate mean of transport when traveling from Shenzhen to Hong Kong on 144 hours visa free transit in Shenzhen. You have to use a ferry instead. You will have to book a ferry through CKS - Chu Kong Passenger Transportation Company website where you will book online, in advance your ticket from Shenzhen Shekou port to Hong Kong Macau Ferry Terminal. Keep in mind that you need this ticket already at the check-in for your flight to Shenzhen in Singapore. You should know that you will have to use that particular ferry that you have bought your tickets for. One more, very important detail. Your stay in Shenzhen has to be at least 25 hours to be allowed to do the above mentioned, i.e. to be allowed to use 144 hours visa free transit. So, please, just plan accordingly.

Ellen, if you are a Singaporean citizens, then you don't have to bother with these details because you can travel as you wish because Singaporeans can travel to China visa free for up to 15 days.

OK, UK citizen... I somehow missed that fact from the title... Then, just follow the instructions in the first post. Apologies.