The Office Of Rail Regulation has said Network Rail must run nine out of 10 trains on time on regional routes in Scotland, London and south east England, while a target of 88% has been also been set for the East Coast and West Coast main lines, the two routes between London and north of the border.
Announcing rail funding for the next five years, the regulator said that by 2019 fewer than three in 100 trains on the West Coast line and about four in 100 on the East Coast line should be hit by cancellation or delays of more than 30 minutes.
The requirements are backed up by stiff financial penalties for railway operators who fail to meet targets, with fines potentially running to millions of pounds.
The Office Of Rail Regulation (ORR) also increased funding to close about 500 level crossings and improve safety at hundreds more of the highest-risk crossings. It is giving an extra £32 million, meaning the total available is now £109m.
That extra funding comes a short time after the House Of Commons Transport Committee heard of concerns about level crossing safety from the parents of Olivia Bazlinton, 14, who, with her friend Charlotte Thompson, was killed at a crossing at Elsenham, Essex in December 2005.
In April 2012, Network was fined £1m over the Elsenham deaths and in April this year the company was fined £450,000 over the death of Jane Harding, 52, on a level crossing at Moreton on Lugg, Herefordshire, in 2010.
ORR chief executive Richard Price said: "Network Rail has made great strides in improving safety, performance and efficiency on Britain's railways. Supported by significant levels of funding from governments, working more closely with the rest of the industry, and learning important lessons from the past, the company is capable of delivering more for customers and taxpayers."
He added: "This plan for Britain's railways between 2014 and 2019 - informed by the public, consumer groups, governments and the industry - requires a safer, higher-performing and more-efficient railway.
"More level crossings will be upgraded or closed; passengers will enjoy better punctuality and suffer fewer cancellations; customers should have a say in shaping billions of pounds of new investment on the network; and the company will continue to bring down the day-to-day costs of running the railways.
"With increased levels of funding in vital areas such as safety and closer monitoring from the regulator, we expect Network Rail to build on past successes and beat the challenges we have set."
The regulators are also proposing rail users and train operators are given a bigger role to shape the specification and delivery of approved enhancements.
Network Rail's funding includes about £250m to help improve the safety of track workers and to be invested in new equipment and safer working practices.
The ORR has also approved an extra £571m to upgrade structures such as bridges and tunnels.
In total, the company will receive more than £21 billion over the next five years to fund the day-to-day running of the rail network. The ORR will require the company to bring down the cost of running the network by about 20%.
Anthony Smith, chief executive of rail customer watchdog Passenger Focus, said the latest round of funding offered a better deal for travellers and commuters.
He said: "Passengers want safe, reliable train services and more and longer trains to cope with rising passenger numbers.
"This large investment is welcome, and these industry targets should help underpin NR's plans. However, passengers will want to see these revised punctuality targets being met."