How long in advance can I obtain entry permit for Shanghai?

My wife and I will be on a 121-day world cruise on Cunard's Queen Elizabeth, commencing January 10, 2016. The cruise will be in Shanghai for one day on March 13, 2016. I am British, my wife is Danish. Do we need visas? If so, can we obtain them in Brussels, Belgium, where we are resident, 5 months in advance, in October 2015?