Yes it does sound like you have a leak on your supply pipe. It's not hugely difficult to repair in theory, provided your supply pipe is plastic and the leak is accessible (IE in your garden and not under your house). In this instance, all that needs to be done is to dig down to the pipe, which will be buried at between 750mm and 1350mm below ground level. It might be that a trench needs digging, or at least more than one hole. The leaky section would then be cut out and the pipe rejoined.
If the leak is under your house the easiest thing to do is to replace the entire supply pipe, which will mean digging a trench along your garden and boring a hole through to a convenient point, where a new stopcock may be installed. This would not necessarily be in the same place as your old one, and that will depend entirely on your individual circumstances. If the pipe is a lead pipe it should be replaced along it's entire length regardless of where the leak is.
It might be worth checking that the guys who installed the meter haven't messed up and left a leak on one of their joints. If this is the case, you should be able to claim back the cost of the lost water.
As for whether your buildings insurance will cover the cost, that is a question only you/they can answer. Some do, some do not.