The MPs say it is "now impossible" to estimate numbers of migrants in the UK
Existing methods of estimating migration and population figures are not "fit for purpose" say MPs.
The International Passenger Survey, designed to provide data for tourism, now plays a central role in migration estimates, the committee of MPs said.
They said it was "not fit for this purpose" and methods of measuring movement in the UK "unsatisfactory".
The committee said new surveys were needed. The Lib Dems said ministers had "totally lost track" of the population.
In its Counting the Population report, the Commons Treasury Committee accepted that the UK was in a period of "significant population change" which made it harder to estimate numbers of people in each area.
But it said population estimates were "central to every national system of official statistics", used to estimate funding for local government, the NHS and other public services.
Getting them right was therefore "a matter of social responsibility" the report said.
It concluded that the IPS - a survey of a random sample of passengers entering and leaving the UK designed largely to provide tourism and business travel data - was now being "called upon to play a central role in estimating international migration".
"It is clear from the evidence we have received that the survey is not fit for this new purpose," the committee said.
The committee said the Office for National Statistics (ONS) had estimated there to have been only 43,000 short-term migrants in England and Wales between June 2004 and June 2005 - based on the IPS.
But it said, to many that figure was "implausibly low" particularly as, in the year 2005-6, in greater London alone there were 235,640 new National Insurance number registrations.
It said IPS statistics for 2005 on international migration were based on "a very small sample" of interviews - with 2,965 people entering the UK and 781 who left.
It recommended that the IPS be replaced with a new, more comprehensive survey designed to measure international movements.
The report also said methods used to measure populations between each census were also "not fit for purpose" as they mid-year estimates did not include short-term migrants.
It recommended that the new Statistics Authority establish "as an immediate priority" more accurate local population statistics reflecting the effects of internal migration.
It called for the authority to look into using other data sources to measure population figures - such as the National Insurance number register, GP lists and council tax records.
The 2011 census should be the last where population is counted through the collection of census forms, it said - instead data should be gathered throughout the UK to allow more reliable annual statistics.
Sub-committee chairman, the Conservative MP Michael Fallon, said they heard evidence that councils including Westminster, Slough and Manchester had been given reduced funding, because of "inaccurate statistical data".
"It is now impossible to estimate accurately the UK population today. Unreliable statistics make planning impossible. We call on the government to improve the population count as a matter of urgency. "
He told BBC Radio 5 Live the UK was lagging behind other countries when it came to measuring population.
"Other countries have much more modern ways of doing this. They have proper population registers, they have address registers and they know where the population was at the end of last week.
"We seem to have really lost track of our population and nobody really has any faith that the government really knows how many people are here and how many aren't."
Jill Matheson, the director general for statistics delivery at the Office for National Statistics, said some of the trends in the UK's workforce mean that producing accurate figures is a difficult task.
"Traditionally what the population estimates have done is measured usual residents. What we've seen more recently is a lot more very short-term migration and a lot of short-term movement between different parts of the country as well.
Of course we have no register, nobody's required to tell anybody if they're moving, if they're leaving, if they're going to live somewhere else, either for a short period or indefinitely, and that's the challenge."
Professor John Salt, of University College London, an international migration expert, said it was "very difficult" to produce a system that captures the "dynamism" of people leaving and entering the UK.
For the Lib Dems, Chris Huhne said: "This report makes it painfully clear that ministers have totally lost track of something as fundamental as how many people actually live in Britain."