I shall be in Hong Kong for the January 1st for possibly 10 days but would like to escape and see some other places if possible, perhaps go into China. Any suggestions?
If you have 5 days the least expensive bang for you buck is to head to Yangshuo by bullet train. It's a stunning area full of Karst mountains, beautiful rivers and loads of cool expats and local Chinese climbers.
You would need to first obtain a 30 day (L) tourist visa for China. You can do this before you leave London.
There are about 12 trains daily from Hong Kong to Guangzhou, you'll want to take the earliest one so that you can transfer the same day from Guangzhou to Guilin.
Once in Guangzhou you'll need to transfer from the East railway station to South railway station. This is easy enough by metro or you can take a taxi.
Once at the railway station in Guilin you can jump on any of the buses outside the train station, there will be plenty of people saying, "yangshuo, yangshuo."
Of course, you can always just fly HK to Guilin for about 300 - 350 USD.
Mentioned in this answer:
if you like body and/or foot massage, pedicure and manicure treatments, Shenzhen is a lot cheaper than Hong Kong :)