Speaking at his party’s conference this week, the home secretary Sajid Javid criticised his own government’s British citizenship test, describing it as like “a pub quiz” that is not fit for its intended purpose.

Javid is not the first to realise this. In 2013, I published what is still the only comprehensive report into the citizenship test, in which I criticised it in those terms – and this was discussed in parliament. So it is pleasing to see my campaign for changing the test has the home secretary on board.

It’s about time. The test is a key part of the immigration system for permanent settlement. Over 2 million tests have been sat since it launched in 2005. Immigrants sit a multiple choice exam with 24 randomly selected questions and must get 18 or more correct to pass the exam. It costs £50 for each attempt – and one person was known to take it 64 times.

The test’s intended purpose is to help confirm that an immigrant has successfully integrated into British society. This might be thought best achieved by checking for any criminal record or tax arrears over an extended residency period (which are also part of the process), but the test is supposed to add something extra beyond this. And here it categorically fails.

If you pour over the roughly 3,000 facts covered by the test questions, including about 280 historical dates spread over 180 pages, it is difficult to see what practical use the citizenship test has. Its handbook does not say how to contact emergency services, register with a GP or report a crime. There is no mention of 999 or of how many MPs sit in the House of Commons. But you must know how many elected representatives sit in the Welsh Assembly, Scottish Parliament and Stormont in Northern Ireland. The handbook requires memorising the height of the London Eye and the age of Big Ben. And while you must know about starting a free school, there is no mention of the national curriculum.

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Unsurprisingly, the test is regularly seen as the test for British citizenship that few British citizens can pass, with many migrants seeing it as an opportunity by the Home Office to extract increasingly more expensive fees through a test of random trivia meant to make more fail.

Instead of ensuring new and old citizens were coming together, my research found the test was actually moving them apart – and doing more harm than good at confirming integration.

In June this year, a House of Lords select committee on citizenship and civic participation agreed with me, endorsing seven of my recommendations, including the need for a new test and an advisory group engaging with the public to close the gap between public expectations and what any such test should cover. While Javid’s remarks acknowledge the citizenship test’s problems that the Lords select committee and I raised, it is unclear what he proposes to do about it. He says the test is not enough, but then promises to bring in “a British values test” as something new.

My concern arises from one difference that I have with the home secretary: I have sat the citizenship test and know it firsthand. If Javid examines the test, he will see that it already does ask immigrants about “the liberal, democratic values that bind our society together”. So if he wants the UK citizenship test to do this, the good news is it already includes it.

It would be a mistake to rush towards launching a new values test or revising the current one without engaging with the public. There are concerns about immigration and how well it is managed that have remained strong for several years. An edict based on guesswork won’t build confidence, especially for those most anxious about immigration levels. One problem shouldn’t lead to something worse.

Now is the time to foster healing for a country divided many different ways beyond the Remain and Leave split. An advisory group, preferably led by a naturalised British citizen who understands the process firsthand, could play an important role in bringing citizens together to discuss what British values we have, what they mean to people and how they can help rebuild a post-Brexit immigration system. Such work could be done over a few months, serving as a useful means for fostering confidence while dispelling immigration myths that might remove some of the toxicity from the debate and move the conversation on.

But it would take courage to make such a new start – and we can only hope such a plan is in mind.