CrossCountry operates a train from Southampton to Cotswolds hourly. Tickets cost $40 - $60 and the journey takes 47 min. Great Western Railway also services this route hourly. Alternatively, National Express operates a bus from Southampton to Cotswolds 3 times a day. Tickets cost $10 - $14 and the journey takes 2 h. 2 other operators also service this route.
From Southampton Central train to Reading, train to Moreton-in-Marsh, then walk to Cotswolds. 2 h 43 min £66. From Southampton bus to Oxford City Centre, George Street (Stop B2), bus to Chipping Norton, Town Hall, bus to Moreton-in-Marsh, Wellington Inn, then walk to Cotswolds. 4 h 51 min £19. From Southampton drive to Cotswolds. 1 h 46 min £17.