The taskforce will investigate complaints by EU nationals living in the UK who fear they will not be allowed to continue living in Britain when the country exits the EU.
Figures show there has been almost a 50 per cent increase in the number of EU citizens applying for permanent UK residency documentation since the referendum on 23 June. The number of applications rose from 36,555 in the three months to June 2016 to 56,024 in the three months to September.
EU nationals in the UK say that to obtain permanent residency cards they have to complete an 85-page form requiring huge files of documentation, including historical household bills and a diary of all the occasions they have left the country since settling in the UK.
Some say that they have received letters inviting them to prepare to leave the country after failing to tick a box on a form.
Labour has urged the UK government to make a commitment that EU nationals currently living in the UK would be free to continue to do so after Britain exits the EU, but Prime Minister Theresa May has, so far, refused to do so.
Dutch MEP Sophie in 't Veld, who is heading the group investigating the residency issue, said the UK government had acted immorally in failing to offer security to those who had made Britain their home.
The ALDE deputy said, "We are receiving so many emails every day from people in the UK and elsewhere who are worried about the future that we cannot answer them individually. This is immoral. And if this leaked document is right, then it has backfired."
As part of the inquiry, a European Parliament hearing is expected to be announced, at which a UK minister will be asked to give evidence. The issue will be debated in Parliament on 1 March.
It is still not clear what the exact consequences of the Brexit referendum vote will be for the thousands of British expats living Brussels and Belgium.
While it will be up to each member state to decide whether British citizens are allowed to carry on living within their respective borders after 2019 - when the UK is expected to formally leave the EU - an internal document drawn up by the parliamentary taskforce says, "the fact that it appears to be difficult for foreign nationals even if married to UK nationals or who are born in the UK to acquire permanent residence status or British nationality may colour member states' approach to this matter."