UK methods of measuring immigration are "wholly inadequate" and must be improved if ministers are to take control of the issue, say peers.
"Flawed" sample surveys used to calculate net migration mean ministers risk formulating policy "in the dark", the House of Lords report concludes.
The government has pledged to reduce net migration - estimated to be 248,000 in 2016 - to 100,000 or less.
It says it is working to improve statistics on EU nationals in the UK.
The pledge to reduce net annual migration - the difference in the number of people coming to the UK for a year or more and those leaving - to the tens of thousands was included in the 2010, 2015 and 2017 Conservative manifestos.
Neither Theresa May nor her predecessor David Cameron has come close to meeting it as prime minister. The most recent figure was 273,000. The last year it was below 100,000 was 1997.
The House of Lords Economic Affairs Committee report pointed out there was already uncertainty over net migration figures, which are based on "extremely poor" data and "flawed" sample surveys.
"Without greatly improved statistics, the government will be formulating policy in the dark," it warned.
Current methods include the International Passenger Survey, a sample survey used as the basis for net migration figures which had a margin of error of 41,000 people at the last count.
The IPS is calculated using figures collected by interviewing between 4,000 and 5,000 passengers a year at 19 airports, eight ports and the Channel Tunnel rail link - less than 1% of whom are identified as immigrants or emigrants.
But the report said the small sample size raised doubts about its reliability and officials acknowledged that some groups are under-represented and students leaving at the end of their degree courses are not accurately counted.
'Bear the burden'
Another method, the Labour Force Survey, had a 50% response rate, did not include those living in communal households and may underestimate short-term migrants, while using National Insurance numbers issued as a measure was also uncertain as many people registered for them, but left after a short period.
The report said the government should use information relating to the economic activity of immigrants - such as taxes or benefits - to better understand how long they remain in the UK.
It said: "Increasing reliance has been placed upon the migration statistics to formulate and judge government policy.
"Many of the available measures are wholly inadequate. In particular the long-standing and widely identified problems with the International Passenger Survey mean that it cannot bear the burden placed upon it and cannot be relied upon to provide accurate estimates of net migration."
The report warned that an "implementation period" for businesses to adapt to fewer EU migrants would be "essential" and it warned that reducing immigration could mean higher prices for consumers.
Committee chairman Lord Forsyth said: "Businesses will have to accept that immigration from the European Union is going to reduce and adapt accordingly.
"Some firms will need to raise wages to attract domestic workers. In other sectors, where migrant workers may not easily be replaced by domestic workers, firms will need to change their business models or increase capital investment in automated processes. All these options may lead to higher prices for consumers."
And the report also said having an annual target for net migration "runs the risk of causing considerable damage by failing to allow the UK to respond flexibly to labour market needs and economic conditions". It says the aim of reducing migration should be "implemented flexibly" instead.
A government spokesman said: "We are collaborating with the Office for National Statistics to develop a system which provides a richer statistical picture of EU nationals in the UK.
"The government is also working to develop a future immigration system which acts in the country's best interests and we will ensure businesses and communities are given the opportunity to contribute their views."
He added that the independent Migration Advisory Committee would be asked to provide evidence on EU migration "precisely because we want strong evidence on which to base these important decisions".