The June survey found 63 percent of people are aware of the concept of net zero, although only four percent know a lot about it.
Almost two-thirds of people have heard of moves to cut emissions to "net zero" and four-fifths are concerned about climate change, official polling suggests.
The latest round of surveying for the Business Department's public attitudes tracker was conducted online - instead of face-to-face as in the past - because of the coronavirus pandemic.
The pandemic also curtailed face-to-face surveys in the previous round in March, with some people questioned online.
Surveying in early June, during lockdown, reveals 81 percent of those questioned are very or fairly concerned about climate change, up slightly from the online responses in March which showed 78 percent were worried about it.
To tackle climate change, the government has brought in a legal target to cut greenhouse emissions by 100 percent on 1990 levels by 2050, described as "net zero".
This requires huge cuts to UK pollution from power, transport, heating and other sectors, and any remaining emissions from hard-to-tackle areas such as flights and farming will have to be offset, for example by planting trees.
The June survey found 63 percent of people are aware of the concept of net zero, although only four percent know a lot about it, and almost a quarter (23 percent) know hardly anything but have heard of it.
Some 12 percent think they know a fair amount and 25 percent said they know a little about net zero.
It is an increase, however, on the online polling in March, the first time the question was asked, when just over half of people (52 percent) said they had some level of awareness.
At that time, just three percent said they knew a lot about net zero, 10 percent said they knew a fair amount, 20 percent a little and 19 percent hardly anything.
Officials said the online results from June and March cannot be directly compared with previous quarterly rounds of surveying, dating back to 2012, which were done face-to-face.
The survey also shows that high support for renewables continues, with 80 percent in favour and just two percent opposing the clean technologies.
Opposition to fracking continues to outweigh support for the controversial process of extracting natural gas, the polling shows. More than 2,500 people were surveyed on Kantar's online omnibus in March and more than 4,000 in June.
Emily Beament is the PA environment correspondent.