Energy suppliers face rising costs for putting smart meters in millions of homes, adding pressure on firms to raise household bills further next year.

Fitting the meters, which automate readings and government has set a target of installing in every home and small business by the end of 2020, costs suppliers about £100 per household today.

But that will jump by nearly a third to £130 in 2018 as companies spend more time and money trying to contact harder-to-reach customers, according to one of the big six suppliers.

However, the entire cost is not expected to be passed on to consumers. When five of the big six did increase their tariffs in the first four months, several blamed smart meters. ScottishPower said smart meters accounted for £10 of the £86 bill increase for millions of its customers.

A source at one energy supplier, who did not want to be named, said the higher cost related to smart meters was due to “customer apathy, concerns and the difficulty in getting people to agree to have a meter fitted”. Staff were having to contact more people, more times, to achieve successful installs, they said.

Householders typically need to take a day off to be at home over a four-hour period for an engineer to swap in a smart gas and electricity meter.

A ramp-up of the smart meter rollout is planned next year, to close the gap between the 7m fitted so far and the 53m needed within four years.

Smart meters were not included in the calculations made by the regulator Ofgem when it warned in January that the rising costs facing suppliers did not justify price hikes.

When five of the big six did increase their tariffs in the first four months, several blamed smart meters. ScottishPower singled them out for £10 of the £86 bill increase for millions of its customers.

Some of the companies were annoyed the cost of the meters had been excluded from Ofgem’s index, which they believe was as a result of political pressure from the Department of Business, Energy and Industrial Strategy. Ofgem denied the claim.

British Gas, which has fitted half of all the 7m smart meters, was the only one of the big six to hold prices in winter, freezing them until 1 August. However, the UK’s biggest energy company is understood to have faced rising costs and is expected to increase tariffs soon.

On Monday, government officials denied there had been any rowing back on the target to fit a smart gas and electricity meter in every home and small business by the end of 2020.

The Conservative manifesto promised only to “offer” one to everyone, a downgrading of language from 2015 manifesto pledge for suppliers to ensure everyone had one by the end of 2020.

That led to speculation that the target – backed by financial penalties for suppliers if they miss it – was being softened.

But Oliver Sinclair, head of engagement for the government’s smart meter programme, told the Guardian: “There’s been a bit of misinformation in the media … Nothing has changed.”

The written shift was because the 2015 manifesto “could imply you had no choice to have a smart meter”, he said. But he said the regulatory obligation on suppliers still stood: “It remains 2020. It remains to try and ensure there is a meter in every home.”

“We’re expecting to see smart fridges that can be turned off remotely during periods where the system needs balancing [energy supply and demand]; smart washing machines or dishwashers; electric vehicles that provide storage,” he said.

EDF, which was criticised in April for raising prices a second time – just days before ministers were expected to announce a price cap, called smart meters “very important [for] rebuilding trust with energy suppliers”.

But Jim Butler, who heads the group’s smart meter programme, said there was a “tremendous amount left to do” on the rollout and the company had installed around 250,000 so far.

British Gas denied it had been targeting easiest customers, such as early adopters, to keep costs down. “I’m not sure we’re picking the low-hanging fruit. The installs are being done for customers who are eligible,” said Steve Briggs, who runs the supplier’s programme.

More than 1 million smart meters were installed in the first three months of 2017, a record rate and 10% higher than the previous quarter. Figures due out on Thursday will show whether the industry has kept up the pace.

A spokesperson at the department for business, energy and industrial strategy said: “Ofgem is an independent regulator and BEIS cannot influence what is included in its Supplier Cost Index. Energy suppliers do have to make upfront investments to purchase and fit smart meters but once installed they will then help reduce energy bills. Smart meters will take £300 million off bills in 2020 alone.”