The statistics watchdog has vowed to resist any political pressure over the release of migration statistics in the run-up to June's EU referendum.
Details of the number of EU migrants paying tax and claiming benefits in the UK will be published next month.
Sir Andrew Dilnot, the chair of the UK Statistics Authority, told MPs that any interference in the process from any source would be "just inappropriate".
But MPs suggested officials didn't have a full picture of migration levels.
Giving evidence to the Public Administration Select Committee, Sir Andrew was questioned about statistics used by the Leave and Remain campaigns during the campaign so far.
He said it was "legitimate" for the Remain campaign to say that 3.3 million jobs were linked to trade with the EU but it would not be fair to say they were directly connected to the EU membership and to claim they would disappear if the UK voted to leave.
Sir Andrew said Leave campaigners were entitled to cite the £19.1bn figure for the UK's gross annual contribution to the EU budget but he was concerned that by stating that the UK could save £350m a week by leaving the EU, this "could be interpreted as implying that the gross figure was, in fact, a net figure" - ignoring the rebate and funds which flow from the EU to the UK.
Sir Andrew, a former director of the Institute for Fiscal Studies, was asked by several MPs about the move to release data on the number of National Insurance numbers actively used by EU citizens in the run-up to the EU referendum on 23 June.
Eurosceptic MPs have long sought more information about this, arguing official figures on inward migration from the EU based on the International Passenger Survey (IPS) underestimate the true numbers.
Sir Andrew told MPs that while it was already known how many NI numbers were issued, it was not known how long recipients were staying in the country afterwards and whether they entered the country with the specific purpose of registering for tax and benefits or whether they were already here.
"It is conceivable the work being done will show the Nino (National Insurance numbers) and IPS numbers are consistent with one another but measuring something different," he said. "It is conceivable that they will not show that... and we will make a judgement about we think about their quality."
National insurance data
Asked by Leave campaigner Kate Hoey whether he had been subject to any pressure from Downing Street or elsewhere in government about the information, Sir Andrew said no.
Asked what would happen if he was, he replied: "If anyone was to put pressure on us they would receive the response that that is just inappropriate and if they continued I would ring the chair (of the committee)."
Eurosceptic MPs have been pushing for information about the number of EU nationals who have paid income tax and NI and received benefits over the last year to be published, as well as information about the nationalities of new NI applicants over the past four years.
They say details of National Insurance numbers - which are issued to those entitled to study or work to help pay tax and benefits - being actively used will shed more light on the current impact of EU migration on the UK labour market.
Figures published by the Office for National Statistics suggested that 257,000 EU migrants came to the UK between September 2014 and September 2015. But other figures for the same period show 630,000 National Insurance numbers were allocated to EU nationals, up 7% on the year before. Of these, 209,000 were from Bulgaria and Romania.
Former Welsh secretary Cheryl Gillan questioned whether any figures would show the true scale of immigration into the UK.
"We are really not in control of this. We really don't have the information about who is coming in, who is working, who is staying and who is leaving...and we don't have the knowledge with which to work."