Assuming your central heating is not supplied from an open-flued appliance, you should be fine to block up the vents if they were solely for the hot air system you mentioned, or are not designed for a gas fire should you have one of those.
Depending on the property, you can also experience condensation due to lack of ventilation. I would recommend doing a bit of research to find out exactly what the vents are for before making any decisions.
RE UPDATE;
If it is open-flued, the flue (The large pipe that comes from the boiler and terminates outside) will incorporate a cone-shaped section which is designed to draw air from the room in order to create drag for combustion gasses to exit the building. If the warm air system was replaced with a central heating system, the chances are it is not open-flued as they are now illegal to install.