There are regular trains from London Victoria to Chichester Station. Trains to London Waterloo connect at nearby Havant Station.
From the Chichester Station you can take a taxi to Spire Cottage which is just under two miles away, or get the No 51 Bus from the bus station to Hunston (get off opposite the Spotted Cow Pub) and continue walking towards Selsey and turn left into Church Lane. Spire Cottage is the first house on the left.
Or, if it’s good weather and you haven’t got too much luggage, walk along the towpath from the Canal Basin in Chichester to Hunston. This will take about 30 minutes.