Killing grass(on purpose)

Hi all
My allotment has grass strips of about one foot to divide each section up. I only have a quarter plot and one of my fellow allotmenteers suggested I get rid of the grass to make a larger growing space and also would eventually mean less work for me as I don't have a law mower and use shears to trim the grass. I can completely see his intentions and thought I might go for it. Can I use weed killer to just kill off the grass? Would this make it easier to dig the grass up? Help?,
MrsW

You could try putting a tent up on it.........That always seems to kill the grass in my back garden

mrswashi - don't you mean teepee!!