If you have an Ideal Standard toilet it is not easy to get a new flush handle. It’s often the plastic bush inside the tank that breaks making the handle go floppy. The standard size for the bush is 1/2 inch but Ideal Standard toilets have a 3/8 bush. The only place I could find a replacement with both sizes was Toolstation.
Job done for a mere £6.51! Always turn off the water before starting. Don’t attempt repairs if you don’t feel confident.