There will certainly be a charge and it might turn out to be a very big one.
There are two possible reasons why there's a 60A fuse in your supply. Firstly, it's possible that the cabling which runs to your house can cope with providing 100A but the cabling which feeds the street couldn't cope if everyone in the street used 100A simultaneously. (So the load is limited by limiting everyone to 60A). In which case, switching the fuse so that just your house can have a 100A supply would probably be a very simple task which would take one man less than an hour to complete.
However, there's a second possible reason why you might have a 60A fuse. It could be that the cabling which feeds your house can't cope with more than 60A. If so, the fuse can't be replaced without replacing the cabling which feeds it. This would involve digging up part of your garden and probably the street as well. That might take a team of men a full day's work, resulting in a very large bill.
You need to contact the company which runs the electricity supply network for your area. The chances are that this is a different company to the one that you pay your bill to. (For example, I pay British Gas for my electricity but the supply network for this area is operated by EDF Energy Networks). Look at your electricity bill (under 'Loss of Supply') to find out the name of the relevant company for your area.
Chris