Linda, either call a plumber
(not the one your neighbour had because a blocked toilet has nothing to do with a dripping overflow)
or ask a friendly local person - and old retired chap who would be pleased to help for free or the price of a couple of beers
OR do it yourself...
The overflow will either come from the toilet cistern (easiest to fix) or possibly from a cold water storage tank in the loft space.
Work out from the dripping pipe where it goes to - you think it's the bathroom - lift the lid of the WC cistern and flush it a couple of times. As the water drains away a float lowers in the water and as the water comes back in the float is lifted on its arm and the movement eventually closes the inlet valve - all very simple.
Pull up on the lever arm and see how the water shuts off. If you can adjust the float then move it further down into the water so that the valve shuts off sooner. There's often a little nylon adjusting screw with a locking nut that bears against the inlet valve - if you screw it in towards the valve that will be the same as lowering the float. Adjust the water level to be an inch or so below the overflow pipe.
It's not difficult.
Good luck...
An old retired chap, July 2009