Connie, if the new kitchen units have not been fitted, then it's very unlikely that the worktops would have been cut. That's one of the last jobs. The units need to be in place before any measuring can be done.
This is a mess, and you really haven't been treated well at all.
With Argos, you have three choices.......
Cancel the order and be refunded
Plenty of time before delivery, so ask if it can be postponed
Take delivery of the appliances and store them until ready for use.
As far as your fitter is concerned, I would scrap him and start over again.
Granite is easy to cut, it's the finishing (polishing) that is a particularly skilled job. When the new units are in place, the fitter should take measurements; make up necessary wooden templates for odd shaped bits; show where sink cut-outs are to go in, then............. go to a specialist marble & slate company. They'll make it all up for the fitter to simply fix in place.
It really should be that simple :o)