Some 6,500 train drivers at nine rail companies, who are members of the Aslef union, are staging their latest 24-hour walkout in a dispute over pay.
There have been several rail strikes this summer, with unions calling for pay increases in line with the rising cost of living.
But rail companies said they could only fund a pay rise through reform.
Avanti West Coast, Southeastern, CrossCountry, London Northwestern Railway, and West Midlands Railway are running no Saturday services at all, while other operators will have an extremely limited service.
Transport for London has also advised passengers there will be no service on the entire London Overground network - which is operated by Arriva Rail London, whose drivers are part of the strike.
The other operators affected by the strike are Great Western, Greater Anglia, LNER, and Hull Trains.