Trains leave from Waterloo every 15 minutes and take about 75 minutes for the 70 miles. Two an hour are expresses. A taxi from Southampton Central costs about four pounds. See Southwest Trains website for times/fares and res. are not necessary. Board third carriage from rear to be near Way Out to get a jump on the taxi queue
National Express (less expensive and less comfortable) coaches depart from Victoria Coach Station and take about two hours. Taxi fare about the same. See National Express website. Res. required.