Not so sure - The old Thameslink service is the most susceptible to cancellation and general crappiness. Victoria Line to Victoria and then direct to Hove is probably the safest bet.......good that there are lots of options, on the day any one of them might be grim......
I commute daily into London Bridge.....when it's been bad it's been awful, but generally the trains are running more or less on time. If you've already got a ticket I wouldn't spend any more by changing. Is the ticket for a specific train though ? If not, I would just try to get an earlier one...