This is an increase of three percentage points compared with the same period last year and is the joint-highest figure since autumn 2012.
Satisfaction with punctuality and reliability of services rose from 73% to 77% in the past year, and overall satisfaction for passengers in London and the South East improved from 79% to 82%.
Southern Railway - which has been engaged in a long-running row with unions over staffing and driver-only trains - recorded the lowest overall score of 72%, up from 69% last year.
No train company's satisfaction figures declined.
Transport Focus chief executive Anthony Smith said: "These green shoots are fragile and need nurturing.
"This recovery will be under pressure from upgrade works, industrial relationship problems and rising passenger numbers. So the industry needs to keep a relentless, ongoing focus on performance and reliability."
The improvement in Southern's performance was boosted by increased satisfaction with the availability of on-board staff and staff at stations, Mr Smith said.
He added: "There is some way to go to reach a more acceptable position. Southern, Thameslink, Great Northern and Southeastern have the lowest scores."
Jacqueline Starr, managing director of customer experience at the Rail Delivery Group, representing train operators and Network Rail, said: "Rail companies are working together to make journeys better and we are pleased to see more satisfied customers.
"There is more to do which is why we are investing to improve and better connect communities across the country with major upgrades to the rail network, thousands of new carriages coming on track and 6,400 extra services a week by 2021.
"We will also continue to work hard to provide better information to our customers, simpler fares and a more accessible railway for all."
Labour's shadow transport secretary Andy McDonald claimed it was "disappointing but not surprising" that passenger satisfaction "remains low".
The only category to suffer a decline in satisfaction was personal security on trains - down two percentage points to 75% - although Transport Focus said the figures "may not be completely comparable with previous waves" due to changes in question ordering.
Mr McDonald added: "The results reveal a concerning decline in passengers' sense of personal security, bringing into question the Government's policy of de-staffing and de-skilling the railway.
"With fewer than half of passengers finding value for money in the price of their ticket, it's becoming more difficult for the Government to justify allowing private and foreign state-owned companies to take money out of the system that should be used to improve services or hold fares down."
Mick Cash, leader of the Rail, Maritime and Transport union, said: "These are marginal increases in satisfaction from an abysmal base and coming at the time that key electrification and upgrade works are being cancelled, passengers and staff will be rightly cynical.
"The only solution to Britain's private rail rip-off is public ownership."
Great railway journeys
Great railway journeys
Reaching heights of 3000 feet and going 100 miles the other side of the Arctic circle, this trip links Stockholm and Kiruna, in Norway. Highlights include the longest fjord in the world, Sognefjord, which is 126 miles long and 4000 feet deep. Come in the summer, and you'll experience the meaning of the term, 'land of the midnight sun'. Visit greatrail.com for more info.
There's no doubt that this is the most luxurious way to cross India. A steam engine drags the train out of Delhi for a week-long trip to the royal estate at Rajasthan. Along the way there's canoodling with elephants in the pink city, Jaipur, a camel safari in the desert at Jaisalmer and a tour of Agra's extraordinary Taj Mahal. Visit thepalaceonwheels.net for more.
Beginning in Cuzco (one of South America's most enchanting cities) and winding its way along the path of the Urubamba River, Peru's famous railway line takes in colossal Andean mountains, Inca ruins and llamas galore. And that's before you get to the unbelievable lost city of Macchu Picchu. For more info, visit machupicchutrain.com for info.
Great Rail Journeys offers berths on arguably the greatest passenger train on the planet, the Golden Eagle, for an astounding ride covering 11 time zones. This epic journey begins in Warsaw and ends 8,000 miles away in Vladivostock. Along the way there's a chance to go ice fishing in the world's biggest lake, Baikal, take a troika carriage in Suzdal, lunch out in a traditional Mongolian 'yurt' tent and gape at the golden domes of Yaketerinburg.
The Orient Express is a byword for luxury travel. Traditionally it served Paris and Istanbul, but that's no longer the case. These days it runs between Strasbourg and Vienna, so you'll have to improvise. Four journeys- Paris-Strasbourg, Strasbourg-Vienna, Vienna-Belgrade and Belgrade-Istanbul- will suffice, taking you from the heartland of Western Europe to the gateway of Asia. Truly a journey worth undertaking, 127 years since its maiden passage.
This railway has been in operation since 1893, giving spectacular views of one of Switzerland's most beautiful regions. It climbs from Interlaken to a height of 11332 feet at Jangfraujoch Station. A phenomenal feat of engineering allows the train to enter through the middle of Eiger mountain. From the top you can see as far as the Black Forest in Germany- this is the so-called 'Roof of Europe' after all. Inside the glacier is Ice Palace, an exhibition of ice sculptures. The cost of a return fare is steep - fares are over hundred quid - but well worth it. Visit jungfrau.ch for more.
The Blue Train offers a luxury service crossing South Africa. It takes in Victoria Falls, the haunting barren landscape of the Great Karoo and the incredibly seaside city of Cape Town. And along the way you'll be glued to the window hoping to spot elephants, lions and other wonderful animals in their wild habitat. Visit bluetrain.co/za for more.
If you want a taste of real speed try a ride on Japan's Shinkansens. The latest model of these bullet trains reaches speeds of 186mph. This means you reach Osaka from Tokyo (515 km away) in a mind-boggling two hours and 25 minutes. You can take a Shinkansen all the way across Japan, from Kagoshima in the south-west to Hachinoche in the north-east. Just be sure not to blink. Visit seat61/japan for more.
Beginning in Tangier (the sleazy port which inspired the likes of Paul Bowles, William H. Burroughs and Jack Kerouac) the train stops at the delightful medieval town of Asilah . Then it heads inland from the modern metropolis of Casablanca, home to the stupendous Hassan II Mosque. The closer to Marrakech one gets, the land becomes pinker and barer, until the foothills of the Atlas Mountains- where the magnificent city itself appears in all its glorious weirdness. Visit greatrail.com for more.
This engineering triumph – which cost $90 million and took 90 years to complete – crosses the guava-spotted deserts and canyons of northern Mexico, linking the Pacific Coast and Chihuahua City by way of 87 tunnels and 36 bridges. The Copper Canyon itself features two climactic zones, so sub-tropical forests give way to a cool alpine climate with oaks and pines. for Visit mexicoscoppercanyon.com for more info.
Don't listen to what anyone else says; from Switzerland to Siberia, by bullet train or steam engine, it's still the best way to travel.