The UK will be at increased risk of blackouts over the next two years unless electricity generators are given new financial incentives, according to the Royal Academy of Engineering (RAE).

The difference between the amount of power that can be generated and the possible peak demand – known as the capacity margin – is likely to fall rapidly, a report by the organisation said on Thursday.

Blackouts are still unlikely, and could only occur if there are sudden threats to the system, such as the unplanned shutdown of a power station, problems with the interconnectors that bring gas and electricity to the UK, and a prolonged cold snap. But the report, which was prepared for the prime minister's Council for Science and Technology, found that these events have all occurred in recent years – though not at the same time – and could easily happen again.

John Roberts, the former chairman of United Utilities who led the work, told the Guardian that electricity generators may need to be given fresh financial incentives paid via energy bills to encourage them to avoid power cuts: "You will need to have incentives. Existing gas-fired power plants are not making money. The government needs to speak to these companies and find out what they need to keep generating [electricity]."

He added: "Energy companies have no legal obligation to keep the lights on. There will need to be incentives."

Older coal-fired power stations are due to come out of service in 2015, but new plants are not coming on stream fast enough to make up the gap, and existing gas-fired power stations have been mothballed as they are uneconomic.

Electricity companies are choosing to use coal rather than gas at present, because coal is plentiful and cheap as a result of the massive boom in shale gas in the US, which has displaced coal-fired generation there and sent the excess coal around the world at cut price rates. But most of the existing coal-fired power plants are likely to be taken out of service in 2015, in order to comply with new European Union directives on pollutants.

Many of the UK's existing gas-fired power plants have been mothballed, because they are comparatively more expensive to run while coal is so cheap. Bringing a gas-fired power plant back on stream can take two to three months, but companies are unlikely to do so because of economic reasons. Roberts said the government would need to take action to encourage companies to bring plants on to standby.

But attempts to bribe energy companies to use their spare capacity, after several years of soaring bills, are unlikely to be popular with consumers, especially in the lead-up to a general election in 2015.

The Department of Energy and Climate Change said: "The lights are not going out. The government, National Grid and Ofgem are taking coordinated action to address challenges to security of supply. In the short term, National Grid is consulting on extending the existing system balancing tools to manage any risks in the middle of the decade. In the medium term, we are legislating for a capacity market, which we've confirmed will be delivering from 2018-19. This will help to drive the new investments we need."

The report found that although the power supply is expected to be sufficient to cover the projected levels of demand for the rest of the decade, the supply system is likely to be stretched "close to its limits". The critical danger point is likely to come next year, during the winter of 2014-15, and if there are unexpected events then that increase demand suddenly or disrupt the supply, there could be a crisis.

Industrial users are likely to feel the brunt of any disruption, as the National Grid will try to cut supplies to businesses temporarily, and balance demand and supply in such a way as to prioritise consumers. The company has already put forward plans to reward large electricity users that can turn their factories off during peak power demand, with a view to freeing up capacity across the network.

The situation is likely to prevail for several years, because in 2019 at least four nuclear reactors are also scheduled to shut down. The UK's only new nuclear reactor in planning, at Hinkley Point, is likely to take longer than that to build. "The longer the situation [of low margin] carries on, the more likely it is [that we will have a blackout]," said Roberts.

He said a margin of about 4% generation capacity above demand was needed to make the supply system safe. Current levels are just above that.

The RAE working group conducted theoretical "stress tests" on the UK's electricity system for its research, using National Grid's forecasts of the capacity margin.

The group recommended that the government should resolve the uncertainties over its plans for electricity market reform as soon as possible, as well as setting out a clear policy on the carbon price floor – which ensures companies and generators pay a minimum price for their emissions - and work with industry to "foster a constructive dialogue with the public on energy policy".

But even if these policies are all pursued, the group warned, additional measures will still be needed to stop utilities from taking even more of their gas-fired power stations off the grid.