Ministers say the rises will pay for investment in the rail network.
Trade unions organised protests at stations around the country and called for the rail network to be returned to public ownership.
Labour said those travelling on busy lines could be “clobbered” with rises of up to 9.1% as train companies add extra increases to some tickets.
Regulated fares are those the government controls, and include season tickets, “anytime” single tickets around major cities, and off-peak inter-city return tickets.
They will go up by an average of inflation – as measured by the retail prices index (RPI) for July – plus 1%.
The RPI fell from 3.3% to 3.1% in July, according to official statistics.
Train companies can vary regulated fares by up to 5% above the average 4.1% rise, but fares that go up by more than the average must be balanced by others that rise by less or fall.
David Sidebottom, from watchdog Passenger Focus, said travellers would “shrug wearily” at the news of another rise, adding: “It is crucial… more trains arrive on time, investment in future improvements continues and the basic promises the industry make are delivered.”
Some campaigners say rail tickets are becoming increasingly unaffordable as price rises outstrip wages.
“It's really starting to eat into people's incomes,” Richard Hebditch, from the Campaign for Better Transport said.
Meanwhile, the TUC organised demonstrations at almost 50 stations around the country.
General secretary Frances O'Grady said passengers were “lining the pockets of the shareholders of private rail companies” and the government should look at renationalising the railways.
Where does your fare go?
On average, for every £1 spent on a train ticket:
Track and station maintenance 48p
Train companies' running costs 17p
Leasing rolling stock 11p
Train fuel 4p
Profit for the train companies 3p
via BBC News
It doesn't have to be like this
Publicly owned railways in Europe cost less to run with lower fares. And every penny made on the railways gets reinvested for the benefit of passengers and taxpayers, not shareholders.
Our research shows that £1.2bn a year is squandered through the fragmentation, inefficiency and cash leaking out of the service in the form of profits and dividends as a result of rail privatisation.
That's enough to fund an 18% cut in fares.
Public ownership of Britain's railways could mean lower fares and your money invested in staff and services. That's not only good for passengers and taxpayers but also our economy and our environment.
See more at Action for Rail