depending on what company is doing the works they can have the car lifted and in some cases they make the car owner pay for the lifting service. only know as i used to working in traffic management and have seen it alot .
but also depends what sort of cones they are . are them normal road cones orange? or are they yellow samller no parking cones .
if there normal road cones i dont mean sh*t. mate just leave the car there . but you do have a big comeback if you havn't been letter dropped.