I have a 40cm cupboard to fit my kitchen sink in. I want to know how much space is required around the sink and is the plumbing underneath going to be difficult in this space.

Well, how big is the sink? Yes, the plumbing will be a little difficult. Especially for fat, old men like me. But it can be done. How difficult depends on how things are presently plumbed.

Is there a sink already in place? A drain and supply lines? 40 centimeters is only 16"=/-. About the only sink that small is a bar sink and they are about 15". Won't be much room to work with. Tell us a little more.