Southeastern, which runs services to London Charing Cross via Battle and Tunbridge Wells, is one of the companies in which staff are on strike.
The industrial action will be held today, Thursday (June 23) and Saturday (June 25).
Severe disruption is expected throughout the rest of this week on days when industrial action is not taking place.
Southeastern said only 35 out of its 180 stations will be open.
While Southern Rail staff are not striking themselves, the national action is severely affecting all journeys on Southern Rail, Gatwick Express, Thameslink and Great Northern between today and Sunday.
The RMT union first announced plans for strikes earlier this month.
RMT general secretary Mick Lynch said: "Railway workers have been treated appallingly and despite our best efforts in negotiations, the rail industry with the support of the government has failed to take their concerns seriously.
"We have a cost-of-living crisis, and it is unacceptable for railway workers to either lose their jobs or face another year of a pay freeze when inflation is at 11.1pc and rising.
"This unfairness is fuelling our members’ anger and their determination to win a fair settlement.
"RMT is open to meaningful negotiations with rail bosses and ministers, but they will need to come up with new proposals to prevent months of disruption on our railways."
Hastings and rye MP, Sally-Ann Hart said: “The union-instigated strikes must be viewed through the lens of fairness.
"After rightly being supported by £16 billion of taxpayers’ money throughout the pandemic, and bearing in mind the resulting changes to the way people now use the railway network, proper reform is needed in the industry.
"It is not right or fair for the RMT to continue to ask for taxpayer subsidies without acknowledging this important point, and my focus is on the many workers and businesses in Hastings and Rye that will bear the brunt of the ongoing industrial action which, if the union’s demands are met, also threatens to worsen the inflationary pressures that we are all experiencing too.”
Bexhill and Battle MP, Huw Merriman said: “I am very sorry for the disruption suffered by passengers this week. I applaud Southern staff who vote against industrial action. Alas, their colleagues in Network Rail have gone on strike so this has shut our local network regardless.
"We need everyone who takes pride in our railway to come together and agree a new way forward to secure its future and as well as the jobs which depend on it.
"This means the unions and industry agreeing on reforms which invests in technology. We can make the railways even safer and more efficient while freeing up money to fund improvements to workforce pay and the passenger experience.
"During the pandemic, a collective effort was made by the Government, industry and workforce to ensure our trains carried on running to get our essential workers to hospitals and other workplaces.
"In France, Spain and Italy, there is a legal requirement for between a third and a fifth of train services to continue to run during a strike. If the strikes continue, we will need these new laws to ensure that our railway and local economy are not damaged.”