More and more garments are labelled 'dry clean' on the care instruction label, but not because more fabrics actually need to be dry cleaned.
Manufacturers are labelling clothes as 'dry clean' because they haven't tested them in washing machines. So have a look at the fibres listed on the label.
Plain, unlined cottons: should be safe to wash at a low temperature with a slow spin speed, but always check first for colour fasness and be aware they may shrink.
Polyester and mixed fibres should be ok too.
Good Housekeeping