Drill a hole through the kitchen floor at the desired location with a cordless drill and a 3/8-inch drill bit. If your floor is fitted with ceramic tiles, stick a strip of masking tape over the tile and use a masonry drill for this operation.
Go into the basement or crawl space and drill 3/8-inch holes through the floor joists between the hole in the floor and the nearest electrical junction box. Drill the holes as close to the kitchen floor as possible. This allows the electrician to trace the circuit from the junction box to the electrical panel, and then replace the existing circuit breaker switch with the required GFCI circuit breaker.
Run a length of the correct amperage 3-core wire from the junction box through the holes in the floor joists, and up through the hole in the floor. Secure the wire to the kitchen floor with insulated cable staples hammered in at 2-foot intervals.
Drill any holes necessary in the island for the electrical wire before installing the island. Measure and mark the hole for the GFCI outlet on your island. Drill 1/4-inch holes in the corners and cut out the opening with a saber saw.
Thread the wire up through the island to the cutout. Position the island correctly. Secure the end of the wire to the outside of the outlet opening with a piece of masking tape. Attach the island to the floor as recommended by the manufacturer.
Call a licensed electrician to install the GFCI circuit breaker on the electrical panel, and to complete the junction box and island GFCI outlet connections.