Southwest Trains runs a train from London Waterloo to Winchester which departs about every 15 minutes on weekdays and Saturdays and fewer on Sundays. The trip takes about one hour if it is an express train, though during peak times they trains also stop along the way at the Basingstoke station and a few other stations along the way.
The train running back to London is on the same schedule, though I would suggest checking with the National Rail before travelling because strikes, track problems and weather can affect the schedule.
Trains from London Waterloo are fast and frequent, taking only an hour on the fast train, or slightly longer on the stopping service.
They are operated by Southwest trains and are normally modern rolling stock with buffet facilities.
Train is the best way to explore area and the city is on the direct line from London’s Waterloo (1 hour). Before arrival to the U.K, we bought Britrail Days Out of London Passes. Our passes gave us opportunity to travel 7 out 15 days in standard (second) class for $142 per person. The pass covers trips in the Southern England including London, Windsor, Portsmouth, Lymington, Cambridge, Oxford, Winchester, and Salisbury.
Winchester train station is about a mile northwest of the cathedral on Stockbridge road.
From here you can walk down Station Rd. and reach Westgate in 7 minutes or so.
Winchester has regular train service to and from London. Go to the UK Railways web site below to plan your trip. It's a lot better than driving. Besides, Winchester has an acute shortage of good parking.