It follows a campaign by commuters for a later rush hour service in the evening to help ease overcrowding.
Other Thames Valley services will have more carriages with first class compartments converted for use by standard ticket holders. There are also extra trains between Swindon and Westbury.
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Ambulances with patients inside had to wait for hours outside Queen Alexandra Hospital in Portsmouth over the weekend.
Monday evening's forecast for the west of the region
Monday evening's forecast for the east of the region