Ireland will remain an open door to the UK for EU citizens after Brexit with no mandatory passport checks on those who travel to Britain via Dublin and Belfast, it has been confirmed.

After Brexit, EU citizens not already settled in the UK will be subject to immigration rules but will be able to travel to Britain via Ireland and Northern Ireland uninhibited.

This is because the withdrawal deal states the UK will respect Ireland’s continued membership of the EU and its freedom of movement rules while at the same time keeping the common travel area (CTA), which has allowed British and Irish citizens to move freely between each others’ countries since 1922.

This means EU citizens, who after Brexit will be classified as third-country immigrants in the UK, will be able to travel to Dublin and on to Belfast and take a domestic flight or ferry to Britain without passport checks.

The revelation came as tensions over the future of Northern Ireland intensified, with the Democratic Unionist party MP Sammy Wilson claiming the withdrawal deal was a “punishment beating”.

Ireland’s deputy prime minister, Simon Coveney, criticised Wilson’s comments, saying: “That kind of language doesn’t help anyone and reminds us of a time we are moving away from.”

Ireland has made a strategic decision to stay out of the fray over the Brexit deal, and Coveney told members of the Irish parliament it would be wrong to try to influence events in Westminster.

The UK Home Office says the UK and Ireland will maintain a high level of cooperation on border security to ensure legitimate travel is facilitated while those who intend to abuse the arrangements are prevented from entering.

However, it is far from the once-mooted scenario where Dublin border officials would have provided the British with details of immigration as a first filter to potential onward travel to Britain.

Under the withdrawal agreement, family members of EU citizens will also be free to travel to Ireland unimpeded as part of the routine freedom of movement rules.

The agreement states the UK “shall ensure that the CTA and the associated rights and privileges can continue to apply without affecting the obligations of Ireland under [EU] law, in particular with respect to free movement for [EU] citizens and their family members, irrespective of their nationality, to, from and within Ireland.”

Sources stress that simple freedom of travel does not equate to rights to jobs or social benefits, and point out that the UK would still have control over immigration through controls in the workplace and welfare regime.

The Home Office said: “As is the case now, people will be able to enter the UK from Ireland without passing through a routine immigration control. However, they are nonetheless always required to meet the UK’s immigration requirements.”