Are you absolutely sure its leaking from the group head or portafilter?
There is a possibility that the boiler gasket is leaking, and water is running down around the sides of the head. Scale is pretty amazing stuff and can work its way betwen the boiler and base, and then the gasket perishes sufficiently to cause a small leak.
Make sure you dont touch anything electrical while doing the following!
If this is the problem, you will be able to see the leak if you remove the top and use a torch to take a look down around the base of the boiler when the machine is on, and often where the bolts are. There may even be signs of corrosion on these.
Worth a look - again though, just be careful.