The Northern Ireland Affairs committee seldom attracts the attention of most of Westminster. Caroline Nokes changed that yesterday – and not in a good way.

The immigration minister's appearance before the committee has been generously described as a car crash: she admitted to never having read the Good Friday Agreement and said, wrongly, that Irish citizens had to be treated as third country nationals in Northern Ireland. To say it was unbelievable, though, would imply that we can expect better from most other ministers. It’s not clear we can.

There was, however, the faintest flicker of good news: Nokes guaranteed the rights of Irish people to live and work freely in Britain more or less as if they were British citizens, rights which predate either country's membership of the EU, would remain unchanged after Brexit.

Asked by Conor McGinn, the Newry-born Labour MP, whether Irish citizens resident in Great Britain would have the right to remain after Brexit – with all of the benefits and privileges they enjoy now – Nokes gave a one-word answer: yes.

She then went on to flesh out that commitment:

“Two elements. Firstly, I am very conscious that we take our obligations very seriously and I am very conscious that for Irish citizens who will continue to have the rights – not Irish citizens who are here today, but Irish citizens full stop – will still be able to come and go as they always have done under protected rights that date back to 1922 and the Common Travel Area and that we regard them as settled from day one, that they have all of the access to benefits and services, and that will be enduring. We take that very seriously.”

Her comments amount to the government's most categorical guarantee of unchanged rights for Irish citizens in Britain after Brexit yet. But not quite in the way Nokes thinks.

Though it might not seem the biggest of deals within the context of the wider Brexit mess, the difficulties in preserving the unique settlement the Irish enjoy in Britain is a running sore. Dublin and Brussels have sought guarantees that it will continue after Brexit, but ministers like Nokes don't seem to understand what this will actually mean.

The government's official position – restated by Nokes yesterday – is that the rights of the Irish in Britain are guaranteed by the Common Travel Area and the Ireland Act of 1949, which stipulated that neither Ireland nor its citizens were foreign for the purposes of UK law.

Here the good news story starts to fall apart. The Common Travel Area is a political agreement. It is non-binding and confers no legal rights upon Irish or British citizens. Contrary to what Nokes and the government appear to believe, its continued existence after Brexit won't guarantee that the Irish in Britain "have all of the access to benefits and services" they have now, just a preferential migration regime.

Nor will the 1949 act, which the government cited in its position paper on Ireland last summer. It has been branded a "dead letter", by migration experts, who have warned it is unlikely that the courts would accept it exempts the Irish from the terms of subsequent immigration legislation.

The inconvenient truth appears to be that most of the actual, legally-watertight privileges enjoyed by Irish people in Britain instead flow from EU citizenship. A report by leading migration barrister Simon Cox found in November that the existing settlement is a "patchwork that may fall apart under post-Brexit political and practical pressures" and said it was impossible to identify a single legal right explicitly conferred on Irish nationals by the 1949 act.

The rights to live, work, access the NHS for free, claim benefits and welfare, and that of British citizenship for children born to Irish parents will all be legally unclear should the government choose merely to keep things as they are in legal terms. Ditto the rights of Irish citizens who arrive from outside the CTA to live and work in the UK.

Perhaps most alarmingly, there would be nothing, said Cox, to legally prevent Britain from excluding or deporting Irish passport holders from the North, including those born there (his report alleged this would contravene the clause of the Good Friday Agreement which enshrines the right of people in Northern Ireland to identify as Irish, British, or both). In this context, Nokes' claim that the Irish had to be third country nationals in the UK is even more concerning.

The situations in which these shortcomings might be exposed might have previously been dimsissed as merely hypothetical. Not so since Windrush exposed the baleful consequences of the hostile environment. Nokes' unambiguous commitment to guaranteeing the rights of Irish citizens will require more than preserving the ramshackle status quo. The bottom line is that, save for selectively ignoring immigration law for the 381,000 Irish nationals in Britain alone, new legislation will be needed to achieve it.

Those campaigning on the issue, like McGinn, are determined to hold the government to it. Dublin will likely do so too. With nearly a dozen pieces of Brexit legislation already choking the legislative timetable before exit day, the government could soon find it has made another rod for its own back.