Consumers face paying half a billion pounds more than expected for the rollout of smart meters and the programme has no chance of hitting its deadline, the UK’s spending watchdog has warned.

The National Audit Office said that with 39m old-fashioned meters yet to be replaced, there is “no realistic prospect” of meeting a goal of all homes and businesses being offered one by the end of 2020 as planned.

In a damning report on the £11bn infrastructure project, the group said that energy suppliers were expecting just 70-75% of households and small businesses to have a smart meter by then.

The NAO urged the government to consider whether a new deadline should be adopted. An influential group of MPs said they would examine whether ministers should stick to the 2020 timetable.

Smart meters automate readings in an attempt to make energy use easier for householders to understand and are considered a critical upgrade of the energy system.

Amyas Morse, the head of the NAO, said: “Costs are rising, and timescales slipping, but smart meters can still succeed over time.”

Labour said the report was evidence the government had failed and had created a “fiasco” with a botched rollout.

The NAO said bill payers would be hit with an increase in costs over the rollout of £500m above the government’s last estimate, or an extra £17 per household.

However, the watchdog said that estimate was conservative and the true cost was likely to be much higher. The extra £500m, for example, does not include energy companies’ marketing costs.

The NAO also noted that the central body established to handle data from meters, run by the outsourcing firm Capita, had already incurred costs of £329m, 69% higher than expected.

The cost of the scheme could have been reduced if the government had chosen to take a “simpler, lower-cost approach”, the group said.

The report was strongly critical of the government allowing 12.5m first-generation smart meters, known as SMETS1, to be installed – more than twice as many had been expected by this point.

Around 70% of SMETS1 meters “go dumb” when customers switch energy supplier, and nearly 1m are operating in dumb mode, meaning those households still have to manually submit readings.

“This means that many consumers will face a choice between remaining with a more expensive tariff or losing the benefits of their smart meter,” the NAO said.

By comparison, the number of second-generation meters, which do not suffer problems after switching and have greater functionality, has been a tiny fraction of what was expected.

Just 109,000 such SMETS2 meters have been installed so far, rather than the 23m expected by now.

The report also laid bare the geographical divide in the rollout. Just 3,000 of those second-generation meters have been installed in the north of England because of technical problems in the region.

Rebecca Long Bailey MP, the shadow business secretary, said: “What should have been an uncontroversial technology has been mired in costly delays and self-defeating technical mistakes.”

Consumer groups urged a rethink of the 2020 deadline. Gillian Guy, chief executive of Citizens Advice, said: “We firmly believe that 2023 is a more reasonable timeframe. This would allow technical problems to be fixed and to ensure that consumers get the best experience.”

The energy minister, Claire Perry, said: “We’ve said everyone will be offered a smart meter by the end of 2020 to reap these benefits and we will meet that commitment.”

Smart Energy GB, the body tasked with promoting the meters, said the rollout was an essential but “hugely complex and challenging infrastructure upgrade”.