UK passport holders qualify for the 144hr visa free entry to Shenzhen? If not how much for VOA?

Mary, you can use 144 hour visa free transit scheme, but in that case you will be required to take a ferry from Hong Kong to Shekou port in Shenzhen and after that to take a ferry from Shekou port in Shenzhen directly to Macau. When you reach Macau, you can return to Hong Kong.

Also, it is important to understand that, if you decide for this option, you will have to buy a ferry ticket from Shekou to Macau through TurboJet website even before you depart from Hong Kong. Also, you will have to print out that ticket and have it in hand, ready to be presented to Shekou immigration. Also, you will have to take exactly that ferry you have bought your ticket for while still in Hong Kong.

If this seems to annoying, you are advised to rely on 5 days Shenzhen VOA. Current price is 130 CNY in cashless form (all major cards are accepted). You cannot take a direct train from Hong Kong West Kowloon station to Shenzhen, but you will cross the border at Lo Wu / Luohu border crossing by taking a suburban train from Hong Kong to Lo Wu.

You need just your passport. At Luohu visa office you will fill out the form, the photo will be taken there and you will pay 130 CNY visa fee. You are strongly advised to be at the border crossing at least at 08:30 to avoid the major queues because Luohu visa office opening hour is 09:00. The visa office is open until 16:30, but you may not be accepted for processing if you arrive at some later hour.

When you are done with your visit to Shenzhen, you can return to Hong Kong by any border crossing and by taking any mean of transport, high speed train included.