Energy customers who reject new smart meters have been warned that the cost to them of maintaining "relic meters" will be "very high".
Climate Change Minister Lord Duncan told MPs that consumers determined not to have a smart meter in their home would face a "quite significant" stick as rollout reached the planned 85% by 2024.
Asked by the Business, Energy and Industrial Strategy Committee what incentives landlords and households would have to switch to the new meters, Lord Duncan said: "Once you have an 85% smart network the cost of maintaining the operation of the non-smart meters is significant, and that's the individuals that have to go and visit, the call centre handlers, and so on.
"There's every possibility that at that point it will become more expensive to hold a non-smart meter so you'll see a disbenefit immediately insofar as it will cost you more to maintain the old-fashioned installation rather than the new one.
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"So I think you will find the stick and it will become quite significant as you move forward, because, once you get to the point of moving down from 15% to 10% to 9% and so forth, the expense of maintaining these relic meters will be very high."
Asked if he was confident that 85% rollout would be achieved by 2024, Lord Duncan replied: "Yes."
Pressed further with the question "What if we don't?", he replied: "We will."
He said energy suppliers who failed to reach their rollout targets would face financial penalties, and added: "There will be an awful lot of climate protesters glued to the side of their building if they are literally failing to meet what will be a moral obligation to help with climate change."
Last month the Government revealed that energy suppliers have been given an extra four years to roll out smart meters into every home in the country, due to delays in connectivity and issues arising with the batch already in use.
The Government also revealed that it predicts only half of households will have a smart meter by 2020 and that the cost of the rollout will rise from £11 billion in 2016 to £13.5 billion today - although total savings will also rise from £16.73 billion to £19.56 billion.
The number of smart meters in homes has risen steadily over the past few years, although the speed of growth has slowed more recently as problems start to arise.
One of the biggest issues has been older generations of meters not working when a household has switched suppliers, with the data no longer being sent in real time to suppliers.
The Government-backed DCC is supposed to be installing infrastructure to ensure the older meters work and that technology is in place so newer versions can connect to the shared networks.
Ministers had previously insisted the 2020 deadline for the rollout was achievable, despite industry warnings that the technology was not ready.