Well in theory we can but it is my understanding that no UK registered aircraft are allowed to fly pure RNAV arrivals (ie. a route made up of points that are not defined by a radio aid) and approaches that take the a/c below sector safe. Geneva now has such a procedure and we don't fly it unless it's VMC.
It's less to do with the accuracy of the equipment than with the accuracy and integrity of the database and the information used to produce it, don't know what other countries allow.