There are delays of up to 30 minutes on CrossCountry trains between Southampton Central and Brockenhurst due to a signalling problem at Redbridge.
First Great Western and South West Trains services are also affected. It is hoped that a normal service will resume from around 6.30pm.
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Tuesday afternoon's weather for the west of the region
Tuesday afternoon's weather for the east of the region
Two private citizens have already paid a "significant deposit" to take the week-long trip.