How can I fix my leaking loo cistern?

My Ideal Standard toilet cistern was filling very slowly and I unscrewed the ball cock to see if there was some obstruction. When I replaced the ballcock float (inserting the rubber washer/grommet correctly I think - it will only go one way because of a 'spike' on one side) the cistern won't stop filling and the overflow continuously leaks into the toilet bowl.
How can I fix this?