The Home Office is warning EU nationals held in detention centres that they should leave the UK to “avoid becoming destitute”, in the latest instance of a hardened tone towards citizens from European countries.

A government letter, written on behalf of home secretary Amber Rudd and seen by the Observer, also advises EU nationals that they should consider leaving because they have the “right to travel freely across the EU and can visit, live, study and in most cases work in any other EU member state” – an observation that appears to preempt the UK’s departure from the union.

The letter, dated 18 October and written by officials from the Home Office’s immigration section, tells a Romanian national in an immigration detention centre that his request for emergency accommodation has been rejected and he should consider another country. It states: “You could avoid becoming destitute by returning to Romania or another EU member state where you could enjoy access to all your ECHR [European Convention on Human Rights] without interference.”

The ECHR protects the human rights and freedoms of individuals in 47 countries belonging to the Council of Europe and prohibits a range of unfair and harmful practices.

Detentions and enforced removals of EU citizens from the UK have risen sharply since the Brexit vote, prompting critics to claim that the Home Office is deliberately targeting EU nationals as part of the “hostile environment” Theresa May pledged for those she believes should not be in the country.

Analysis of government data shows deportations of EU citizens are at their highest since records began, with 5,301 removals in the year to June 2017 and a policy of deporting European nationals accused of sleeping rough.

Celia Clarke, director of the legal charity Bail for Immigration Detainees (BiD), said: “One of the worrying aspects of the Home Office letter refusing an EU national entitlement to accommodation to enable him to apply for bail to get out of detention is its tone: effectively telling a detainee to go home or go to another EU country.

“If UK officials are acting in this way towards EU nationals now, the future of our relations with EU nationals and countries should be a concern to us all. The danger is that the divorce from the EU is becoming ever more acrimonious, and this is reflected in both the tone and the practice of the Home Office.”

Despite coming under considerable pressure, May has held off promising to maintain EU citizens’ rights until those of UK citizens in the rest of the EU have been secured. Last Thursday, however, the foreign secretary, Boris Johnson, attempted to reduce disquiet by telling a meeting of Polish dignitaries their rights would be “protected whatever happens” after Brexit.

Meanwhile, other documents spell out a further potential headache for May’s leadership. A letter from the European commission’s directorate-general for justice has indicated that it is serious about investigating the increased detention of EU nationals in Britain and whether UK authorities are restricting “their right to move and reside freely”. It has begun the process of asking for evidence on the issue.

The letter, dated 20 October, also reveals that the commission is “looking into the amendments of UK law” that came into force in February and have since been routinely used to deport EU citizens. According to the contentious law changes, individuals found to have been sleeping rough can now be “subject to administrative removal” from the UK.

“These regulations seem to have created the conditions for a cavalier approach towards the detention and removal of EEA nationals,” said Clarke.

The Home Office declined to comment, saying only that the “description of the letter provided is not one we recognise as a Home Office document”.