Reseed Existing Lawn

Something like this would do ye?
http://www.wilko.com/lawn-seed+food/wilko-aftercutting-lawn-food-35kg/invt/0300378

By the way , does putting grass cuttings on top of the lawn do any benefit to it? or is it just a Myth

 

Also can i just put the grass seeds on top of the dead lawn without adding any top soil or fertilser? Will it grow correctly?

Someone just mentioned to me i may need to rake and remove the dead weed and grass then put seeds on top.