An e-petition calls for ministers to do “everything necessary” to stabilise numbers and keep them well below the landmark figure.
Last week, national statisticians warned the UK will surpass Germany as the largest EU nation within a generation thanks to the fastest population growth since the baby boom.
The official projections said, on current trends, the 70 million mark will be reached by 2027, two years earlier than previous estimates.
More than two thirds of the rise will be due to immigration, both directly and indirectly.
The e-petition has been launched by Migration Watch UK, which campaigns for lower immigration, and it hope to generate enough public support to earn a debate on the floor of the House of Commons.
Two other petitions on high-profile issues have already won such a debate, one on papers relating to the Hillsborough disaster and one on an EU referendum.
Sir Andrew Green, chairman of Migration Watch UK, said: “Labour permitted foreign immigration of over three million in the face of public opinion.
“Politicians need reminding that this is an issue that is consistently one of the top concerns of voters and that it must be addressed, and soon.
“It is time to stop listening to those who support and, often, make money from the immigration ‘industry’ and consider the views of the people most directly affected.
“This, at last, is an opportunity for the man in the street to make their views heard where it counts.”
The e-petition system was created by David Cameron as part of his drive to make politics more accessible to the public.
Any petition that receives more that 100,000 signatures is sent to the Commons Back Bench Committee, which can select it for a debate in parliament.
Last month Mr Cameron was rocked by a rebellion of 81 Conservative MPs who demanded a referendum on Britain’s membership of the EU, as a result of an e-petition.
The resulting debate ended in a vote, which the Government comfortably won but not without suffering the largest ever Tory revolt on Europe.
In September, relatives of victims of the Hillsborough disaster won a key victory when a debate saw MPs called for all documents on the incident to be released.
The latest petition comes amid growing concern over the size of the UK population and the impact of immigration.
The Office for National Statistics said the UK population will hit 74 million by 2043 taking it past Germany which is expected to fall from 81 million to just over 73 million.
Two thirds of the rise will be due to either direct immigration in to the country or migrant mothers giving birth.
The projection is based, in part, on an annual net migration, the difference between those arriving and leaving, of 200,000. Last year it was 240,000.
Officials estimate the population will swell by 0.8 per cent–or 491,000–every year to 2020, the fastest sustained growth since the 1960s.
It is a fresh headache for David Cameron who has pledged to bring immigration down to the “tens of thousands”.
The Migration Watch e-petition reads: “Over the past ten years the government has permitted mass immigration despite very strong public opposition reflected in numerous opinion polls. We express our deep concern that, according to official figures, the population of the UK is now expected to reach 70 million within 20 years with two thirds of the increase due to immigration.
“While we recognise the benefits that properly controlled immigration could bring to our economy and society, this population increase, which is the equivalent of building seven cities the size of Birmingham, will have a huge impact both on our quality of life and on our public services yet the public has never been consulted.
“So we call on the government to take all necessary steps to get immigration down to a level that will stabilise our population as close to the present level as possible and, certainly, well below 70 million.”
It can be found at http://epetitions.direct.gov.uk/petitions/19658.