London could see riots again unless more trains and buses are provided at affordable fares for the poorest communities as the population soars, the city's transport commissioner has warned.

He said the city will face "overwhelming" overcrowding on its congested transport networks by 2030 without urgent progress on new rail lines.

Despite an annual investment of about £1bn in tube upgrades and the £14.8bn spent building Crossrail, a rapidly expanding population means an additional 6m trips will be made in the capital each day by the end of the next decade, swallowing up the new capacity on public transport.

In an interview with the Guardian, Sir Peter Hendy, head of Transport for London, said low-paid workers now lived on the outskirts of the capital rather than in inner-city neighbourhoods, and that there could be "social unrest" if they could not easily commute around the city for work.

"London's poor don't live in Harrow Road, they live in Enfield and Tolworth and if you can't get them to jobs they want, your city's going to be in a bad way: it's not going to progress and contribute to national economic growth," Hendy said. "The stakes are pretty high. If you're not able to increase transport capacity, and people find accessing work impossible, you risk social unrest. You can expect trouble."

Bus fares have risen by more than 50% in six years under the London mayor, Boris Johnson – a policy Hendy has backed. But the transport commissioner he warned fares could not continue to rise. "The bus network is the staple of outer London. We're going to need more revenue funding. Otherwise we're going to leave people behind. When you start leaving people behind, you start saying to people in London they may not be able to get to work on time and when that happens, you damage the economy quite severely."

Hendy also warned that unless major infrastructure projects, such as Crossrail 2, were started and new rail lines were built, overcrowding in central London would be "overwhelming". Transport chiefs say it will take at least 15 years to build Crossrail 2.

"You just won't be able to get into or on to many of our transport networks at peak times if you don't start [these infrastructure projects] now. When Crossrail opens, it will be full within months; the population will go on towards 10 million and you'll soon need Crossrail 2. You won't be able to do without it. In central London the overcrowding will grow to be overwhelming."

London's population is officially estimated at 8.4 million and is rising by about 80,000 people a year. It is expected to reach 10 million by 2030. "If you contemplate a London in 2030 without continuous investment and more revenue money, we will have the kind of congestion you're looking at in Mumbai," he said.

Mumbai was one of several Indian cities that experienced protests over rail fare increases earlier this year, while more than a year of escalating demonstrations in Brazilian cities in the runup to the 2014 World Cup were ignited by fare rises on public transport.

While the completed Crossrail, a revitalised Thameslink line and tube upgrades will bring great leaps in capacity in the next five years, transport chiefs are struggling to keep up with passenger numbers, which have risen by a third on the tube in the past 10 years. The underground ran more services and carried more customers than ever before in 2013-14, with a record 1.265 billion passengers.

The capital's growth was putting pressure in places that "people never expected", Hendy said. "I've been a strong advocate of putting fares up a lot in an era of declining government funding. But if the poor are not living in Tower Hamlets, Stockwell, Hackney and Southwark any more and all the places where people on low incomes used to live, they are living a long way away and a future mayor is going to have to make sure they can afford to get to work."

The chancellor, George Osborne, cut funding for day-to-day operations in London by 25% in the last spending review, meaning fares are likely to rise in coming years. Hendy and TfL will be joining with counterparts in Transport for Greater Manchester in the coming weeks to push for greater powers over revenue and spending for cities. Hendy said TfL was already unable to match the rising demand for buses. "The choice as we look forward is not whether people come to London, but if you have enough revenue to cope with them and whether the people who do the poorer paying jobs can access them.

"In 2016, unless there is more money we will start leaving people behind. We've had a 1-2% increase in mileage every year with a fairly substantial reduction in subsidy. The growth in bus demand has far outstripped the mileage because we haven't had the money."

Transport chiefs believe pressure on road space is likely to be even more intense than on the rail and tube network.

Michele Dix, director of planning for TfL, said: "We'll have to manage it radically better or provide new space. We're looking at more of the space being in tunnels – putting certain vehicles underground. We don't want to generate more traffic. As many people we can get to walk, cycle or use public transport we will."

Dix said road tunnel schemes, primarily designed for freight vehicles and deliveries, were an option TfL was considering. One proposal for a 22-mile inner orbital tunnel has been published, including subterranean dual carriageways, although Hendy said the timescale for completion was likely to be decades.

Dix said any such schemes would be tightly controlled to deter a rise in private car use. Both TfL and independent transport experts argue that increased charging for road access seems inevitable.