Ministers could potentially consider some type of post-Brexit ID card system for the UK, the immigration minister has said, saying this would be a response to the sheer complexity of residence rules once free movement ends.

Giving evidence to the EU home affairs subcommittee in the House of Lords, Caroline Nokes said particular difficulties could arise in the event of a no-deal Brexit, as there would be seven separate ways under which EU nationals could legally be in the UK.

“I very much hope that we do not … but I’m conscious that we may well end up in a no-deal situation,” she told the committee.

Calling herself “a fan of free movement”, Nokes said: “We are ending free movement, that is what we have chosen to do, because of the very clear direction we were given by the British people in the referendum of 2016. It is more complicated and there are no two ways about that.”

She was asked about ID cards by Timothy Kirkhope, a Conservative peer who was an immigration minister in John Major’s government.

Nokes said the idea had come up during talks with groups representing EU nationals in the UK, some of whom came from countries where ID cards are normal.

“We are from a different culture where ID cards have never been the British way,” she said. “But at times people can make quite compelling, interesting arguments to me about ID cards.”

Nokes said she personally opposed the idea, adding: “However, it has been very apparent to me over the course of the past few debates that we’ve had about immigration in the Commons, from the evidence sessions for the immigration bill committee, that there is a growing body of opinion on this – I can’t venture into the Commons without somebody screaming at me, ‘Isn’t it time you introduced ID cards?’

Caroline Nokes: ‘ID cards have never been the British way.’ Photograph: Henry Nicholls/Reuters

“So it’s not our policy, it is not what I wish to do. But certainly in the case of EU citizens who might in their home member state have been used to them, I can see that there is some argument in favour.”

Under earlier questioning from the crossbench peer Peter Ricketts, Nokes accepted a no-deal Brexit would bring particular complexity in working out whether or not EU nationals had the right to stay in the UK.

Ricketts said he had counted six ways under which people could stay if there were no deal: indefinite leave to remain, settled status, pre-settled status, transitional one-year visa, European temporary leave to remain for three years, and three months without leave.

Nokes agreed and added a seventh – people who were legally in the UK before departure under free movement and had not applied for any subsequent permission to stay. This all meant, she said, that it was “absolutely imperative” the UK had a departure deal with a transitional period.

Nokes said any post-Brexit enforcement regime would be “light touch”, and allow for the fact that the system had changed substantially.